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         Number Theory:     more books (100)
  1. New Developments In The Additive Theory Of Prime Numbers by Jianya Liu, 2008-06-30
  2. Pythagorean Theory of Number by Manly P. Hall, 1993-01-01
  3. Number Theory: Volume I: Tools and Diophantine Equations (Graduate Texts in Mathematics) by Henri Cohen, 2007-05-23
  4. A Concise Introduction to the Theory of Numbers by Alan Baker, 1985-01-25
  5. Multiplicative Number Theory by Harold Davenport, 2000-10-31
  6. Elementary Number Theory in Nine Chapters, Second Edition by James J. Tattersall, 2005-07-25
  7. Analytic Number Theory (Graduate Texts in Mathematics) by Donald J. Newman, 2000-07-19
  8. Algebraic Number Theory (Chapman & Hall Mathematics) by Ian Stewart, David Tall, 1987-05
  9. Advanced Number Theory by Harvey Cohn, 1980-08-01
  10. Number Theory (Pure and Applied Mathematics) by Z. I. Borevich, I. R. Shafarevich, 1986-05
  11. Essays On The Theory Of Numbers by Richard Dedekind, 2007-07-25
  12. The Theory of Algebraic Number Fields by David Hilbert, 1998-10-01
  13. History of the Theory of Numbers, Volume ll: Diophantine Analysis (History of the Theory of Numbers) by Leonard Eugene Dickson, 2005-06-07
  14. 250 Problems in Elementary Number Theory (Modern analytic and computational methods in science and mathematics) by Waclaw Sierpinski, 1971-03-26

101. Number Theory
number theory at the Mathematics Dept. of the University of Texas. Permanent faculty in number theory, and their fields of interest.
Number Theory at the Mathematics Dept. of the University of Texas
Permanent faculty in Number Theory, and their fields of interest.
  • Frank Gerth ): Algebraic number theory, including class numbers, class groups, discriminants, class field theory, density theorems, Iwasawa theory.
  • John Tate ): 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 ): 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.
  • ): 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.
Computational projects
(computo, ergo sum)
Introduction Projects Software Contact ... [Up] (The Latin locution was found in the home page of David Bailey
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

103. Title
Part of the Euler Project.
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 Chantal David cdavid
Organizer for 2003-2004:
Andrew Granville
Chantal David
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

105. Research In Number Theory & Combinatorics
number theory and Combinatorics. Staff, research interests.
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
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 ...
  • 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.
    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: 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

    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.
    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
    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.
    History of Arithmetic and Number Theory See also the history of numbers and counting.
    On the Web
    • 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).
    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
    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
    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.
    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.
    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).
    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.
    C R A N T S
    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.
    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).
    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.
    AMS Special Session on
    Cryptography and Computational and Algorithmic Number Theory
    Ohio State University, Columbus Ohio
    September 21-23, 2001
    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."
    Eric Bach , University of Wisconsin at Madison,
    Jon Sorenson
    , Butler University,
    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
    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.
    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
    Last update made Fri Feb 27 15:22:13 EST 2004.
    March 21-23, 2003
    University of Florida, Gainesville
    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
    • 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
    [Click on speaker's name to view title and abstract and slides (if available)]

    119. (UK) Nottingham University
    number theory and Arithmetic Geometry research group. Research interests, members, visitors, meetings.
    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.
    From September 6th to December 20th 2004 (Version française)
    Organizing Committee Karim Belabas Henri Cohen John Cremona Jean-François Mestre ... Don Zagier Contact


    ... 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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