1. Algebraic Number Theory Archives Electronic preprint archives for mathematics research papers in algebraic number theory and arithmetic geometry. algebraic number theory Archives. http://www.math.uiuc.edu/Algebraic-Number-Theory/

Algebraic Number Theory Archives Date: Wed, 8 Jan 2003 12:03:33 -0600 (CST) To: Algebraic-Number-Theory@listserv.uiuc.edu Subject: Algebraic-Number-Theory preprint archives I shall no longer be managing the Algebraic Number Theory preprint archives. The web site is now frozen and is not accepting new submissions and subscriptions. Michael Zieve has kindly agreed to assume control, with the help of Greg Kuperberg, and new submissions should be directed to the new URL for the archive, http://front.math.ucdavis.edu/ANT/ Your subscription will continue, unless you choose otherwise. I thank Dan Grayson for setting up the archives and his patient help with technical issues, and Michael and Greg for volunteering to take on this work. Nigel Boston http://www.math.wisc.edu/~boston/ Welcome to the preprint archives for papers in Algebraic Number Theory and Arithmetic Geometry. Use the Find facility of your browser on this page, or search: Our mirror site in the United Kingdom , set up by Richard Pinch. Our main site in the USA Instructions for authors Instructions for joining the mailing list . Members of the mailing list receive announcements of preprints when they are deposited in the archives. Some TeX fonts , stored in a tar image compressed with gzip, including the lams* and xy* fonts, which are needed for some of the preprints.

2. Home Page J. S. Milne. Mathematics site of J.S. Milne; course notes preprints, and other manuscripts. Fields and Galois Theory. Algebraic Geometry. algebraic number theory. Modular Functions and Modular 2003 Corrected version of Fields and Galois Theory. August 29, 2003 Corrected http://www.jmilne.org/math

3. MP473 2000 Samuel, Algebraic Theory of Numbers, QA247.S25131972. algebraic number theory, I.N Mann, Introduction to algebraic number theory, QA241.M31955. P. Ribenboim, Algebraic Numbers, QA247 http://www.numbertheory.org/courses/MP473

MP473 Number Theory IIIH/IVH, Semester 2, 2000 Prepared by Keith Matthews Email: krm@maths.uq.edu.au Web: http://www.maths.uq.edu.au/~krm/ Lecture notes Problem sheets Past exams ... Some informative number theory sites Study Suggestions Students are encouraged in tutorials to raise any difficulties encountered with the problem sheets and lecture material. Students should try to keep up to date with study of their lectures, so as to be able to understand subsequent lectures. They are also urged to do as many problems as possible. By doing problems, students will soon discover their strong and weak points. The lecture notes will contain enough explanations and examples to make the definitions, theorems and arguments clear. However some students will need further examples and explanations of certain points and I recommend they peruse books from the reading list below. Most of these books have lots of examples and develop the concepts in greater detail than we have time for in our short course of lectures. Course Outline The course is an introduction to algebraic number theory, especially quadratic and cyclotomic fields.

4. Algebraic Number Theory Archive Welcome to the (new) algebraic number theory Archive, founded by Nigel Boston and Dan Grayson and This archive is for research in algebraic number theory and arithmetic geometry http://front.math.ucdavis.edu/ANT

Algebraic Number Theory Archive Welcome to the (new) Algebraic Number Theory Archive, founded by Nigel Boston and Dan Grayson and currently maintained by Michael Zieve . This archive is for research in algebraic number theory and arithmetic geometry. It is being converted to an overlay for the mathematics arXiv Instructions for authors: Please contribute new submissions to the NT (Number Theory) category of the math arXiv following these submission instructions . Submissions in algebraic number theory will automatically appear here within a few days. Please send email if your arXiv article has been overlooked. Members of the mailing list receive announcements of new e-prints. To subscribe (or unsubscribe), please write to the Michael Zieve Some TeX fonts in compressed tar format, including the lams* and xy* fonts, which are needed for some of the e-prints. Papers math.AG/0405529 : 27 May 2004, Cyclic p-groups and semi-stable reduction of curves in equal characteristic p>0 , by Mohamed Saidi. math.NT/0405505 : 26 May 2004

5. Algebraic Number Theory Course notes by Robin Chapman, University of Exeter, May 2000. http://www.maths.ex.ac.uk/~rjc/courses/ant99/ant99.html

MAS4002: Algebraic Number Theory This is the home page for the Algebraic Number Theory course. At present it is still under construction. Eventually it will contain copies of course handouts, commentaries on some of my more challenging problems, and useful links. Most files are in dvi format. The course will be closely based on the following book: Ian Stewart and David Tall, Algebraic Number Theory , Chapman and Hall. Alas the paperback is out of print (and the hardback is overpriced) but the following alternative is very cheap (but a bit old-fashioned): Harry Pollard and Harold G. Diamond, The Theory of Algebraic Numbers , Dover. Course information Background on rings and ideals 1998 exam Problem sheet 1 ... Almost complete summary of notes to course (version 5, recently corrected!) Robin Chapman Room 811, Laver Building University of Exeter Exeter, EX4 4QE, UK rjc@maths.ex.ac.uk 2nd May 2000 Back to teaching page Back to home page

6. Courses localization. Introduction to algebraic number theory ps file (432K); Introduction to algebraic number theory - pdf file (193K) http://www.maths.nott.ac.uk/personal/ibf/courses.html

Lecture Notes of Courses (.ps and .pdf files) Introduction to number theory - ps file (495K) Introduction to number theory - pdf file (242K) This is a first course in number theory. It includes p-adic numbers. Commutative algebra - ps file (381K) Commutative algebra - pdf file (202K) This course is an introduction to categories, modules over rings, Noetherian modules, unique factorization domains and polynomial rings over them, modules over principal ideal domains, localization. Introduction to algebraic number theory - ps file (432K) Introduction to algebraic number theory - pdf file (193K) This course (36 hours) is a relatively elementary course which requires minimal prerequisites from Commutative Algebra (see above) for its understanding. Integrality over rings, algebraic extensions of fields, field isomorphisms, norms and traces are discussed in the second part. Dedekind rings, factorization in Dedekind rings, norms of ideals, splitting of prime ideals in field extensions, finiteness of the ideal class group and Dirichlet's theorem on units are treated in the second part. Homological algebra - ps file (479K) Homological algebra - pdf file (228K) This is a very short introduction to homological algebra This course (25 hours) presents categories, functors, chain complexes, homologies, free, projective and injective obejcts in the category of modules over a ring, projective and injective resolutions, derived functors, Tor and Ext, cohomologies of modules over a finite group, restriction and corestriction.

7. Algebraic Number Theory algebraic number theory. algebraic number theory. Math 676.dvi The Finiteness of the Class Number. The Unit Theorem http://www.jmilne.org/math/CourseNotes/math676.html

Algebraic Number Theory Algebraic Number Theory Math 676.dvi Math 676.ps.gz Math 676.pdf v2.01; August 14, 1996; first version on the web; 144p. v2.10; August 31, 1998; fixed many minor errors; added exercises and index; 140p. Contents Preliminaries From Commutative Algebra Rings of Integers Dedekind Domains; Factorization The Finiteness of the Class Number The Unit Theorem Cyclotomic Extensions; Fermat's Last Theorem Valuations; Local Fields Global Fields Solutions for the exercises 676sltn.dvi The final exam for the course 676exam.dvi Errata

8. Title Details - Cambridge University Press Pure Mathematics. algebraic number theory. A. Fröhlich, M a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced http://titles.cambridge.org/catalogue.asp?isbn=0521438349

9. 11R: Algebraic Number Theory: Global Fields Selected topics here 11R algebraic number theory global fields. Introduction. History. Applications and related fields. For complex multiplication, See 11G15 Lang, Serge "algebraic number theory", Graduate Texts in Mathematics, 110 Zassenhaus, H. " Algorithmic algebraic number theory", Encyclopedia of Mathematics and its Applications http://www.math.niu.edu/~rusin/known-math/index/11RXX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 11R: Algebraic number theory: global fields Introduction History Applications and related fields For complex multiplication, See 11G15 The rings of integers in these fields are also studied in Commutative Ring Theory , where we may find discussion of Unique Factorization Domains (UFDs), Euclidean domains, etc. Subfields Algebraic numbers; rings of algebraic integers PV-numbers and generalizations; other special algebraic numbers Polynomials (irreducibility, etc.) Quadratic extensions Cubic and quartic extensions Cyclotomic extensions Other abelian and metabelian extensions Other number fields Iwasawa theory Units and factorization Class numbers, class groups, discriminants Galois theory Integral representations related to algebraic numbers; Galois module structure of rings of integers, See Also 20C10 Galois cohomology, See also 12Gxx, 16H05, 19A31 Class field theory Langlands-Weil conjectures, nonabelian class field theory, See also 11Fxx, 22E55

10. IHP -- Explicit Methods In Number Theory" Research session on effective and computational aspects of algebraic number theory and arithmetic geometry. Institut Henri Poincar©, Paris, France; 6 September 20 December 2004. 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

11. Home Page Of Robert B. Ash Downloadable textbooks for the basic graduate year of abstract algebra, and for introductions to algebraic number theory and commutative algebra. http://www.math.uiuc.edu/~r-ash/

Robert B. Ash Professor Emeritus, Mathematics Dept. of Mathematics University of Illinois 1409 W Green St. Urbana, IL 61801 e-mail r-ash@math.uiuc.edu Books etc. On Line Abstract Algebra: The Basic Graduate Year A Course In Algebraic Number Theory A Course In Commutative Algebra A Pari/GP Tutorial Click below to read/download chapters in pdf format. PDF files can be viewed with the free program Adobe Acrobat Reader Comments and suggestions for improvement are welcome. Abstract Algebra: The Basic Graduate Year (Revised 11/02) This is a student-oriented text covering the standard first year graduate course in algebra. Solutions to all problems are included and some of the reasoning is informal. Front Preface and Table of Contents (110 K) Chapter 0 Prerequisites (194 K) Chapter 1 Group Fundamentals (150 K) Chapter 2 Ring Fundamentals (222 K) Chapter 3 Field Fundamentals (135 K) Chapter 4 Module Fundamentals (357 K) Enrichment Chapters 1-4 (288 K) Chapter 5 Some Basic Techniques of Group Theory (405 K) Chapter 6 Galois Theory (480 K) Chapter 7 Introducing Algebraic Number Theory (410 K) Chapter 8 Introducing Algebraic Geometry(448 K) Chapter 9 Introducing Noncommutative Algebra (350 K) Chapter 10 Introducing Homological Algebra(437 K) Supplement (315 K) Solutions Chapters 1-5 (461 K) Solutions Chapters 6-10 (449 K) End Bibliography, List of Symbols and Index (233 K)

12. Course Notes Lecture notes by ChingLi Chai, University of Pennsylvania. http://www.math.upenn.edu/~chai/coursenotes.html

Course Notes Notes from some of my graduate courses, courtesy of Jeff Achter Algebraic Number Theory, Part I (Math 620, fall 1993) dvi file (.dvi format) or postscript file (.ps format) Algebraic Number Theory, Part II (Math 620, spring 1994) dvi file (.dvi format) or postscript file (.ps format) Introduction to Automorphic L -functions (Math 620, spring 1997) dvi file (.dvi format) Reading Course Notes Notes on Cartier Theory, very preliminary version (.pdf format)

13. Robin Chapman Arithmetic (dvi, ps, pdf); Notes on Algebraic Numbers (dvi, ps, pdf); algebraic number theory (dvi, ps, pdf). Preprints Cubic identities for http://www.maths.ex.ac.uk/~rjc/rjc.html

Robin Chapman's Home Page I'm a lecturer in Mathematics at the University of Exeter . My mathematical interests include number theory, algebra, combinatorics and problem solving. This is how I looked on 20th March 1999. This is my teaching page where you'll find details of courses, undergraduate projects etc. And this is my list of publications I have the following manuscripts available: Lecture notes: A Guide to Arithmetic ( dvi ps pdf Notes on Algebraic Numbers ( dvi ps pdf Algebraic Number Theory ( dvi ps pdf Preprints: Cubic identities for theta series in three variables ( dvi ps pdf submitted to The Ramanujan Journal A probabilistic proof of the Andrews-Gordon identities ( dvi ps pdf submitted to Discrete Mathematics Determinants of Legendre symbol matrices ( dvi ps pdf submitted to Acta Arithmetica Evaluation of the Dedekind eta function (with William Hart) ( dvi ps pdf submitted to Canadian Mathematical Bulletin Miscellaneous articles and surveys: Evaluating zeta(2) ( dvi ps pdf This gives (so far) fourteen proofs that the sum of the reciprocals of the squares of the natural numbers equals pi squared over six. Constructions of the Golay codes ( dvi ps pdf So far this is restricted to the binary Golay code. Eight constructions are given.

14. Notes For Dick Gross' Algebraic Number Theory Course, University Of Utah Taken by Sean SatherWagstaff, Utah, Spring 1999. In PS and PDF formats. http://www.math.uiuc.edu/~ssather/MATH/notes.html

Notes for Dick Gross' Algebraic Number Theory Course University of Utah Spring 1999 During the Spring Semester of 1999, I typed up the notes for the Number Theory Course taught by Dick Gross who visited from Harvard. I am posting the notes only in .ps and .pdf format since some of the files contain .eps figures. If you need a hard copy or something, email me Before I post anything, I get it approved by Professor Gross, but if you find any mistakes, email me All lectures (1-18) compressed notes_all.ps.gz or notes_all.pdf.gz : material from 14 January to 25 March Back to Sean's Homepage Last updated 5.25.99

15. Explicit Algebraic Number Theory Subject. The title Explicit algebraic number theory is borrowed from the series of Oberwolfach meetings on Explicit methods in number theory. http://www.math.leidenuniv.nl/~psh/EANT/

September 23 - October 2, 2002 Lorentz Center , Leiden Instructional part (`Stieltjesweek'): September 23 - 26 Organizers: H.W. Lenstra P. Stevenhagen NWO-OTKA workshop: September 27 - Oct 2 Organizers: P. Stevenhagen R. Tijdeman Subject The title Explicit algebraic number theory is borrowed from the series of Oberwolfach meetings on Explicit methods in number theory . Those meetings are characterized by a lively interaction between abstract and advanced arithmetic theories on the one hand and concrete and elementary questions on the other. The spirit of the present workshop, which consists of 4 instructional days and 4 days of talks by (invited) participants, is similar, but within the smaller compass of algebraic number theory. Instructional part The instructional part emphasizes problems that are inspired by questions from other areas of mathematics, including elementary and algorithmic number theory, arithmetic algebraic geometry, and computer algebra. The advanced techniques from algebraic number theory that apply to these problems include class field theory, infinite Galois theory, and the theory of quadratic forms. The purpose of this part is to impart a working knowledge of these theories to the participants, to provide ample illustrations of their use, and to formulate several open problems that may be approachable by means of the same techniques. Prerequisites : basic algebra, number theory, and point set topology, including Galois theory, algebraic number theory and a knowledge of p-adic numbers.

16. Springer-Verlag - Number Theory & Combinatorics of the basic material of classical algebraic number theory, giving the student the background necessary of further topics in algebraic number theory, such as cyclotomic fields, or http://www.springer-ny.com/detail.tpl?isbn=0387942254

17. 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

18. CRC Press Online played pivotal roles in developing algebraic number theory. Explores in detail the direct, practical application of algebraic number theory to cryptography http://www.crcpress.com/us/product.asp?sku=3989 &dept_id=1

19. Kash KANT / KASH. Computational algebraic number theory / KAnt SHell. KANT is a software package for mathematicians interested in algebraic number theory. http://www.math.tu-berlin.de/~kant/kash.html

KANT / KASH Computational Algebraic Number Theory / KAnt SHell The KANT Group: [members] [publications] [database] ... [ftp] KANT is a software package for mathematicians interested in algebraic number theory. For those KANT is a tool for sophisticated computations in number fields and in global function fields. With KASH you are able to use the powerful KANT V4 functions within a shell and you do not need to know anything at all about programming in C. KASH is freely available. You can pick up the current release of KASH using ftp . You can download the documentation for KASH separately. Most of the functionality of KASH is also available through the web interface webkash . Many of the algorithms, which are implemented in KASH/KANT, are described in the publications of the KANT Group . Take a look at a KASH sample-session (taken from the ICM 98 Mathematical Software Session). Please mail all your questions, suggestions, comments and bug reports concerning KASH to kant@math.tu-berlin.de The main features of the current release are: Computations in number fields arithmetic of algebraic numbers

20. Mathematics Staff Homepage UMIST. algebraic number theory, Galois module structure. http://www.ma.umist.ac.uk/mjt/

Martin Taylor Professor in Pure Mathematics EPSRC Senior Research Fellow Royal Society Wolfson Research Fellow Qualifications: M.A. (Oxford), Ph.D (London). Room No. O15 Administrative duties: Member of EPSRC College, Chairman of Royal Society Scientific Unions Committee Research: Galois, Hermitian and quadratic structure for arithmetic varieties. Publications List CV Other activities: Flyfishing, Hill walking. Professor M J Taylor FRS Mathematics Department, UMIST P.O. Box 88 Manchester M60 1QD UK use + 44 161 200 3640 from overseas Fax: Email: Martin.Taylor@umist.ac.uk

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