101. Number Theory number theory at the Mathematics Dept. of the University of Texas. Permanent faculty in number theory, and their fields of interest. http://www.ma.utexas.edu/users/voloch/numberthy.html

Number Theory at the Mathematics Dept. of the University of Texas Permanent faculty in Number Theory, and their fields of interest. Frank Gerth gerth@math.utexas.edu ): Algebraic number theory, including class numbers, class groups, discriminants, class field theory, density theorems, Iwasawa theory. John Tate tate@math.utexas.edu ): Algebraic Number Theory (local and global fields), Class Field Theory, Galois cohomology, Galois representations, L-functions and their special values, modular forms, elliptic curves and abelian varieties. Jeffrey Vaaler vaaler@math.utexas.edu ): Analytic number theory, Diophantine approximation and the geometry of numbers in local and global fields, Diophantine inequalities, polynomials, effective measures of irrationality and transcendence, applications of Fourier analysis in number theory, inequalities and extremal problems. villegas@math.utexas.edu ): Special values of L-functions (Birch-Swinnerton-Dyer and Bloch-Beilinson conjectures), arithmetic of elliptic curves, modular forms, Mahler measure of polynomials. Felipe Voloch ): Arithmetic of function fields. Diophantine geometry over function fields. Geometry of algebraic curves. Algebraic varieties over finite fields. Modular forms, elliptic curves and abelian varieties. Finite fields and applications to coding theory and cryptography.

102. Computational Projects Virtually all of them are in one way or another related to the theory of numbers. List of available software packages related to number theory. http://www.ieeta.pt/~tos/hobbies.html

Computational projects (computo, ergo sum) Introduction Projects Software Contact ... [Up] (The Latin locution was found in the home page of David Bailey Introduction Long ago, I decided to find interesting problems, usually requiring extensive verifications and/or enumerations, to occupy the idle CPU time of most workstations and personal computers in my working environment. This page presents links to short descriptions of ongoing or finished computational projects I have found interesting and stimulating. Virtually all of them are in one way or another related to the theory of numbers. Most of these pages contain links to selected results of these extensive computations. To save space, download time, and to provide some data integrity checks, these ASCII text files were compressed with the gzip program. These files can be uncompressed using either the gunzip, zcat, or zless programs. Windows users can also uncompress them using, for example, the WinZip or WinRAR programs. As far as I am aware, some of the results reported in these pages are (or were for some time) records of computation. List of available computational project descriptions The 3x+1 conjecture Some generalizations of the 3x+1 conjecture Enumeration of polyominoes and other animals Determination of the minimum width of admissible prime constellations Verification of the Goldbach conjecture ; you can help extend the range of this massive computation Statistics about prime gaps (a by-product of the Goldbach conjecture verification) Tables with values of the

103. Title Part of the Euler Project. http://www.wcsu.ctstateu.edu/~sandifer/eulernotes/numthry.htm

Summary of Euler’s 96 articles on Number Theory I have partly or completely translated the following Number Theory articles, though not all of them are yet available through the Euler Project E-26 – complete translation E-29 - notes with Dick Pelosi 8/5/98 E-54 – complete translation E-100 – complete translation E-152 – partial translation E-158 - sent to Mark Johnson 8/7/98 E-242 – notes E-256 – partial translation E-279 – notes E-449 – notes E-461 – complete translation E-559 – mostly translated (done?) Summaries of the articles Proves that F5 is composite, though he doesn’t give any clues about how he discovered this fact. He also tacks on a few "theorems", but says that he doesn’t yet know how to prove them. th powers can’t be a 4 th power. th powers can’t be a 4 th power and other such forms. p =a p +b p (mod p) and uses this to show again that F5 is not prime. n to denote the sum of the divisors of n. First number theoretic function. Proves many of the basic properties of the function. qbb contentorum A first page footnote by Rudio warns us that Euler says that most of these theorems are known to him only by "induciton." Their proofs appear in other places.

104. QVNTS QuébecVermont number theory Seminars. Organizer for 2003-2004 Andrew Granville andrew@dms.umontreal.ca Chantal David cdavid http://cicma.mathstat.concordia.ca/faculty/chantal/qvnts.html

Organizer for 2003-2004: Andrew Granville andrew@dms.umontreal.ca Chantal David cdavid@mathstat.concordia.ca Thursday morning: 10:30-12:00, McGill University, Burnside Hall 920 Thursday afternoon: 2:15-3:45, Concordia University, Library Building LB-540 Time and location - Burlington Thursday morning: 10:30-12:00, University of Vermont, Mathematics Conference Room Thursday afternoon: 2:15-3:45, University of Vermont, Mathematics Conference Room Schedule of the seminar in and

105. Research In Number Theory & Combinatorics number theory and Combinatorics. Staff, research interests. http://www.maths.gla.ac.uk/research/groups/ntc/ntc.html

Mathematics Home Research Undergrad Postgrad ... Mathematical Education Both number theory and combinatorics are part of what is called discrete mathematics, which has important applications in computer science and information technology, as well as an intrinsic elegance and fascination for mathematicians, professionals and amateurs alike. Number theory In combinatorics one is usually concerned with a finite set with some additional structure (e.g. a projective geometry, a graph or a block-design), and seeks to relate it to some already-known set of the same kind, or perhaps to show that certain structures can (or cannot) be imposed on a given set. Another type of question is the enumeration of particular kinds of structures (e.g. how many connected graphs are there on n vertices?). Current topics of interest in the department include: combinatorial design theory; automorphism groups of graphs and designs; Hadamard matrices and symmetric designs and their classification; applications of combinatorics to computer graphics. The following member of staff are involved in research in Number Theory and Combinatorics: Dr I. Anderson

106. Articles number theory Tutorials. The aim of this section is in the series of tutorials to educate students about main theorems of Number http://matholymp.com/TUTORIALS/numbers.html

Number Theory Tutorials The aim of this section is in the series of tutorials to educate students about main theorems of Number Theory included into the unwritten IMO syllabus. Divisibility and primes Euclidean algorithm Euler's theorem ... Frontpage

107. Welcome To Scott Chapman Trinity University, San Antonio. Commutative algebra, finite abelian groups, combinatorics and number theory especially factorization of elements in integral domains and monoids. http://www.trinity.edu/schapman/index.html

Welcome to Scott Chapman's Web Page Trinity University Department of Mathematics One Trinity Place San Antonio, Texas 78212-7200 Phone: (210) 999-8245 Fax: (210) 999-8264 e-mail: schapman@trinity.edu Information on the Trinity REU Program Last Call for Papers for the Proceedings of the Chapel Hill Conference on Commutative Rings and Monoids. Information for Classes for Spring 2004 All course materials are pdf files and require the Adobe Acrobat Reader. Math 1312: Calculus II Sample Examinations: Test I Test II Test III Final Exam Math 3341: Number Theory Sample Examinations: Test I Test II Test III Research Interests My research interests are in commutative algebra, finite abelian groups, combinatorics and number theory. In particular, I am very interested in problems concerning factorization of elements in integral domains and monoids. You can find a complete list of my publications on my VITA . Here are some recent titles which can be downloaded as pdf files: "On cross numbers of minimal zero-sequences in certain cyclic groups,"

108. IBFI Schloss Dagstuhl - Dagstuhl Seminar 04211 Algorithms and number theory. J. Cremona (Univ. In computational algebraic number theory sufficiently good algorithms for the most important problems are known. http://www.dagstuhl.de/04211/

SCHLOSS DAGSTUHL INTERNATIONAL CONFERENCE AND RESEARCH CENTER FOR COMPUTER SCIENCE Dagstuhl Seminar 04211 Home Page Dagstuhl Seminars Algorithms and Number Theory J. Buhler (Reed College, USA), J. Cremona (Univ. of Nottingham, UK), M.E. Pohst (TU Berlin, DE) Seminar Data Seminar Materials List of participants with talks List of participants with adresses From outside of Dagstuhl this list is only accessible via anonymous login. Use "anonymous" as user id and your e-mail address as password. (Works similar to anonymous ftp.) Seminar Participants Group Picture Seminar Participants Group Picture Description of the planned Seminar Seminars on Algorithmische Zahlentheorie and Algorithms and Number Theory were already held at the IBFI in the years 1992, 1994, 1998 and 2001. The corresponding Seminar-Reports document the success of these meetings. The area of Algorithmic Number Theory is on the borderline between Mathematics (Number Theory) and Computer Science (including Complexity Theory). It has developed rapidly in the last 20 years and important results were obtained. Number theoretical algorithms have become fundamental for many applications in Cryptography, Coding Theory and also for Computer Algebra Systems. The central topics of this seminar will be classical computational number theory, algorithmic aspects of elliptic curves and curves of higher genus, and their applications. Additionally, we plan to discuss new areas in which there have been important developments recently.

109. History Of Mathematics: History Of Arithmetic And Number Theory History of Arithmetic and number theory. See also the history of numbers and counting. On the Web. Mathematics Archive s index to number theory on the web. http://aleph0.clarku.edu/~djoyce/mathhist/arithmetic.html

History of Arithmetic and Number Theory See also the history of numbers and counting. On the Web Mathematics Archive's index to number theory on the web Pages on arithmetic and number theory at the Mathematical MacTutor History of Mathematics archive Prime numbers Fermat's last theorem ... History of Fermat's Last Theorem by Andrew Granville (TeX) Bibliography Cunnington, Susan. The story of arithmetic, a short history of its origin and development. Swan Sonnenschein, London, 1904. Dickson, Leonard Eugene. History of the theory of numbers. Three volumes. Reprints: Carnegie Institute of Washington, Washington, 1932. Chelsea, New York, 1952, 1966. Fine, Henry Burchard (1858-1928). The number system of algebra treated theoretically and historically. Karpinski, Louis Charles (1878-1956). The history of arithmetic. Number theory and its history. McGraw-Hill, New York, 1948. Weil, Andre. Number theory: an approach through history. Birkhauser, Boston, 1984. Reviewed: Math. Rev. Regional mathematics Subjects Books and other resources Chronology ... Home

110. Algebra And Number Theory Algebra and number theory. The KANT Group. KANT stands for Computational Algebraic number theory with a slight hint to its German origin (Immanuel Kant). http://www.math.tu-berlin.de/algebra/

Algebra and Number Theory The KANT Group The KANT Group: [members] [publications] [database] ... KASH/KANT - computer algebra system Immanuel Kant The KANT functions are accessible through a user-friendly shell named KASH (KAnt SHell) which is freely available. You can pick up the current release of KASH using ftp webkash Most of the functionality of KASH is also available through a web interface. KANT Database The KANT database of more than 1.3 million number fields can be accessed through a web interface and through the computer algebra system KASH/KANT Publications You can download the publications of members of the KANT Group. Last modified: 2004-05-24 20:37

111. (UK) King's College, University Of London number theory Group. Staff, meetings, preprints. http://www.mth.kcl.ac.uk/research/numbtheo/

Mathematics Department King's College, University of London Research in Number Theory King's College London has a strong tradition of research in Number Theory and this continues today with a particular emphasis on algebraic and representation-theoretic aspects of the subject. Staff are at the forefront of research in areas attracting international interest. Current projects involve collaboration with workers in France, Germany and the United States. Much of the work done at King's involves L - and zeta-functions in one guise or another, not only the complex versions of these functions attached to number fields but also their p -adic-valued analogues and similar functions attached to local fields. However, rather than study their quantitative and `analytic' properties per se , our interest centres on the extraordinary capacity of these functions for reflecting the fine algebraic structure of such objects as the unit groups, class groups, other K -groups, Galois groups and matrix-groups that occur in the arithmetic of the local and global fields. Indeed, the last 30 years have seen a huge amount of interest by number theorists worldwide in exploiting these links in even more general contexts: for instance the L - and zeta-functions associated to arithmo-geometric objects such as algebraic curves defined over (Galois extensions of) number fields. This has stimulated - and, in turn, been stimulated by some far-reaching conjectures and while much remains mysterious, progress is slowly being made. For example the interplay between

112. Explicit Methods In Number Theory Explicit Methods in number theory. November 13 18, 2004. Information technology industries have shown serious interest in computational number theory. http://www.pims.math.ca/birs/workshops/2004/04w5502/

with the participation of Explicit Methods in Number Theory November 13 - 18, 2004 Organizers: Peter Borwein (Simon Fraser University Department of Mathematics), H.W. Lenstra (University of California Berkeley Department of Mathematics), P. Stevenhagen (Mathematisch Instituut, Universiteit Leiden), H. Williams (Department of Mathematics, University of Calgary). Objectives With this workshop, we intend to provide an opportunity for the participants to communicate recent developments in the various participating disciplines to experts in the same and in neigbouring areas. Furthermore, the workshop will facilitate and promote new and existing collaborations by giving an opportunity for participants to meet their colleagues in a relatively small, informal and intensive environment. Developments in the participating areas are vast and quick. Many collaborations between physically distant researchers are ongoing and new results in one area often spark off new collaborations with researchers in other areas. The proposed meeting will give the participants an excellent platform for disseminating their results to a relevant audience and will give them a chance to absorb results by others. Recent meetings at MSRI and Oberwolfach have shown that the subject area is very much in flux and that there is a clear demand for more opportunities for dissemination and collaboration in this field. Information technology industries have shown serious interest in computational number theory. Many number theoretic constructions find an application in cryptography or coding theory. Furthermore, the computational challenges offered by number theory give an excellent incentive and clear benchmarks for the computing industry to enhance hardware and the constant quest for faster algorithms enhances computational tools in general.

113. C R A N T S A regional seminar for the greater Capital District of New York (the area of Albany, Saratoga Springs, Schenectady, and Troy) devoted to number theory, algebra, and related topics in mathematics. http://math.albany.edu:8000/math/Current/Crants/

C R A N T S CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR Spring Semester, 2004 Jessica Sidman, Mount Holyoke College, April 23 at Univ. at Albany Lindsay Childs, Univ. at Albany, April 28 at Union College Hara Charalambous, Univ. at Albany, May 5 at Univ. at Albany Fall Semester, 2003 Bodo Pareigis, Universitaet Munchen, September 24 at Univ. at Albany Antun Milas, Rensselaer Polytechnic Institute, October 8 at Univ. at Albany Pedro Teixeira, Union College, October 22 at Union College Cristian Lenart, Univ. at Albany, November 5 at Skidmore College Cristian Lenart, Univ. at Albany, November 19 at Univ. at Albany Antun Milas, Rensselaer Polytechnic Institute, December 10 at Univ. at Albany Spring Semester, 2003 William Hammond, Univ. at Albany, February 12 at Univ. at Albany Alex Tchernev, Univ. at Albany, February 26 at Skidmore College Alex Tchernev, Univ. at Albany, March 19 at Univ. at Albany Lindsay Childs, Univ. at Albany, April 2 at Union College Pedro Teixeira, Union College, April 30 at Union College Fall Semester, 2002 Alex Tchernev, Univ. at Albany

114. Diophantine Approximation And Analytic Number Theory with the participation of, with the particpation of MITACS. Diophantine approximation and analytic number theory. November 20 25, 2004. http://www.pims.math.ca/birs/workshops/2004/04w5507/

with the participation of Diophantine approximation and analytic number theory November 20 - 25, 2004 Organizers: Michael Bennett (University of British Columbia), Greg Martin (Department of Mathematics, UBC), John Friedlander (Univ. of Toronto Math Dept.), Andrew Granville (Department de mathematiques, Universite de Montreal), Cameron Stewart (Department of Pure Mathematics, Univ. of Waterloo), Trevor Wooley (Department of Mathematics, Univ of Michigan). Objectives The objective of this workshop is to gather together researchers with expertise in both Diophantine approximation and analytic number theory in an environment that fosters the presentation and sharing of the latest ideas in both fields. The participants named below have been chosen either as experts in analytic number theory whose work involves problems in Diophantine approximation, or as experts in Diophantine approximation whose methods also lend themselves to the resolution of open questions in analytic number theory. As remarked below, we also intend for the workshop to provide a significant learning experience and exposure to current research for number theorists in these two areas in the early stages of their careers. Number theory is unique among the major fields of mathematics in that it combines problems and questions of incredible simplicity and accessibility with truly deep and technical tools and methods for addressing these questions. A reduction of a problem in one area of number theory (and indeed in many other mathematical fields as well) often involves a very simply stated question in the other area, which can seem difficult to resolve if one is not well-versed in the techniques of the second area. Often, contact and communication between Diophantine approximation researchers and analytic number theorists is the greatest obstacle to overcome on the way to significant advances on both sides. This accessibility that number theory possesses is another reason that involving young researchers in the workshop is so profitable.

115. AMS Special Session On Cryptography And Number Theory Ohio State University, Columbus, Ohio; 2123 September 2001. http://euclid.butler.edu/~sorenson/ams.html

AMS Special Session on Cryptography and Computational and Algorithmic Number Theory Ohio State University, Columbus Ohio September 21-23, 2001 Pictures! Announcements Because of the recent tragic events in New York, Washington, and Pennsylvania, several of our confirmed speakers have had to cancel. The AMS has decided to go forward with the meetings, and so shall we: "We plan to go ahead with the meeting at this time and we will dedicate the meeting to mathematicians, their friends and families who have suffered from the horrible events of Tuesday 11th September." Organizers Eric Bach , University of Wisconsin at Madison, bach@cs.wisc.edu Jon Sorenson , Butler University, sorenson@butler.edu List of Speakers Daniel J. Bernstein, University of Illinois at Chicago Larry Gerstein, University of California at Santa Barbara (cancelled) Jon Grantham, IDA/CCS (cancelled) Joshua Holden, Rose-Hulman Institute of Technology Michael Jacobson, University of Manitoba, Canada Jee Koh, Indiana University (cancelled) Kristin Lauter, Microsoft Corporation (cancelled)

116. Future Directions In Algorithmic Number Theory Future directions in algorithmic number theory. This web page highlights some of the conjectures and open problems concerning Future http://www.aimath.org/WWN/primesinp/

Future directions in algorithmic number theory This web page highlights some of the conjectures and open problems concerning Future directions in algorithmic number theory. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. Lecture Notes Agrawal: Primality Testing Agrawal: Finding Quadratic Nonresidues Bernstein: Proving Primality After Agrawal-Kayal-Saxena ... Remarks on Agrawal's Conjecture

117. P-Adic Analytic Number Theory Notes of a short course at the Mehta Research Institute by M. Ram Murty. http://www.mri.ernet.in/~mathweb/lecture/murty-padic00/

MRI Main Page Mathematics Lecture Notes Introduction to p-Adic Analytic Number Theory M. Ram Murty (Queen's University) These are the notes of a short course given at the Mehta Research Institute on $p$-adic analytic number theory from December 22, 1999 till January 12, 2000. I intend to polish these notes and expand them for publication in the MRI Lecture Notes Series. Till such an amplified version becomes available, the concise version may be welcome for a quick study of the subject. Title Page DVI PS Contents DVI PS Preface DVI PS 1. Historical introduction DVI PS 2. Bernoulli numbers DVI PS 3. $p$-adic numbers DVI PS 4. Hensel's lemma DVI PS 5. $p$-adic interpolation DVI PS 6. $p$-adic $L$-functions DVI PS 7. Leopoldt's class number formula DVI PS Last modified: Fri Mar 31 16:16:16 IST 2000

118. Q-CONF Research in number theory Combinatorics Research in number theory Combinatorics. The following member of staff are involved in research in number theory and Combinatorics http://www.math.ufl.edu/~frank/qmiftconf.html

Last update made Fri Feb 27 15:22:13 EST 2004. CONFERENCE ON NUMBER THEORY AND COMBINATORICS IN PHYSICS March 21-23, 2003 University of Florida, Gainesville TRAVEL INFORMATION WEATHER ACCOMMODATIONS MAPS ... PHOTOS THEME The aim of the conference is bring mathematicians and physicists together working in the topics below, to discuss, learn and communicate different view-points. Provisional list of topics q -hypergeometric functions, Rogers-Ramanujan identities, Exact Integrable Models and Conformal Field Theory Enumerative Combinatorics and Lattice Models Alternating Sign Matrices and Determinants Quantum Computing Riemann zeta-function, Random matrices and Quantum Correlators ADVISORY BOARD George Andrews Pennsylvania State University Michael Fisher University of Maryland Steven Girvin Yale Michio Jimbo University of Tokyo Barry McCoy Stony Brook Tetsuji Miwa RIMS, Kyoto Leonard Susskind Stanford Edward Witten IAS, Princeton PLENARY SPEAKERS [Click on speaker's name to view title and abstract and slides (if available)] George E. Andrews

119. (UK) Nottingham University number theory and Arithmetic Geometry research group. Research interests, members, visitors, meetings. http://www.maths.nott.ac.uk/personal/ibf/ntag.html

Number Theory and Arithmetic geometry at Nottingham Click on to go to a new page Information for potential PhD students The group welcomes applications from potential PhD students. Successful applicants will be made an offer of a PhD place by the university. The funding opportunities for EU students include a postgraduate studentship (usually for three years) from EPSRC, which covers all university fees and (for UK students only) a maintenance grant. Alternatively, the school will help with applying to EU Marie Curie Fellowship which can provide support up to three years. In very strong cases, University Scholarships are available to successful candidates. With its large group of researchers working in a spread of related fields within Number Theory and Arithmetic Geometry, Nottingham is a most attractive place for PhD study. Currently the number theory group in Nottingham is the largest in the UK. Students who are at first not sure exactly in which area they wish to work can experience a wide variety of research topics before deciding, and always have the possibility of moving between supervisors. For further details see PhD study in Number Theory and Arithmetic Geometry in Nottingham

120. IHP -- Explicit Methods In Number Theory" place at the Centre Émile Borel and will present state of the art in effective and computational aspects of algebraic number theory and arithmetic geometry. http://igd.univ-lyon1.fr/~webeuler/ihp/ihp-e.html

From September 6th to December 20th 2004 (Version française) Organizing Committee Karim Belabas Henri Cohen John Cremona Jean-François Mestre ... Don Zagier Contact emnt@ihp.jussieu.fr Registration Poster Presentation ... Useful informations Presentation This trimester is to take place at the Centre Émile Borel and will present state of the art in effective and computational aspects of algebraic number theory and arithmetic geometry. Discussions sessions and seminars series will take place during this trimester, as well as short courses on the computer algebra systems MAGMA et PARI/GP. Those interested in participating in the program can register on-line at the following address Participation of predocs and postdocs is strongly encouraged. They will have open access to all the Institute facilities. Those seeking financial support and/or an office should send a letter of application to the secretary , together with a curriculum vitae (and a letter of recommendation for students only). Long courses John CREMONA: Elliptic curves Bjorn POONEN: Rational points on curves Don ZAGIER: TBA (TBA: to be announced) Short courses Le critère de Nyman pour l'hypothèse de Riemann Frits BEUKERS: The equation x p + y q = d z r Manjul BHARGAVA: Higher composition laws Jean-Marc DESHOUILLERS: Explicit methods in additive number theory Effective complex multiplication in small genus and applications to primality proving Eduardo FRIEDMANN: Barnes's multiple Gamma function

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