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         Algebraic Number Theory:     more books (100)
  1. Algebraic Number Theory (Graduate Texts in Mathematics) by Serge Lang, 2000-07-19
  2. Algebraic Number Theory and Fermat's Last Theorem by Ian Stewart, David Tall, 2001-12-01
  3. Problems in Algebraic Number Theory (Graduate Texts in Mathematics) by M. Ram Murty, Jody Esmonde, 2004-10-25
  4. Computational Algebraic Number Theory (Oberwolfach Seminars) by M.E. Pohst, 2004-02-04
  5. Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger by Pierre Samuel, 2008-04-18
  6. The Theory of Algebraic Numbers by Harry Pollard, Harold G. Diamond, 1998-01-12
  7. Algebraic Number Theory and Code Design for Rayleigh Fading Channels (Foundations and Trends in Communications and Information The) by F Oggier, E Viterbo, 2004-12-15
  8. Algebraic Number Theory (Cambridge Studies in Advanced Mathematics) by A. Fröhlich, M. J. Taylor, 1993-02-26
  9. Algebraic Number Theory (Chapman & Hall Mathematics) by Ian Stewart, David Tall, 1987-05
  10. Algebraic Number Theory (Grundlehren der mathematischen Wissenschaften) by Jürgen Neukirch, 1999-06-22
  11. Introductory Algebraic Number Theory by Saban Alaca, Kenneth S. Williams, 2003-11-17
  12. Algebraic Number Theory by H. Koch, 1997-10-16
  13. The Theory of Algebraic Number Fields by David Hilbert, 1998-10-01
  14. A Brief Guide to Algebraic Number Theory by H. P. F. Swinnerton-Dyer, Peter Swinnerton-Dyer, 2001-07-15

1. Algebraic Number Theory Archives
Electronic preprint archives for mathematics research papers in algebraic number theory and arithmetic geometry. algebraic number theory Archives.
Algebraic Number Theory Archives
Date: Wed, 8 Jan 2003 12:03:33 -0600 (CST)
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, 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
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

    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
    MP473 Number Theory IIIH/IVH, Semester 2, 2000
    Prepared by Keith Matthews
    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
    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.
    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.
    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. Robin Chapman
    Room 811, Laver Building
    University of Exeter
    Exeter, EX4 4QE, 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)
    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
    Algebraic Number Theory
    Algebraic Number Theory
    Math 676.dvi

    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.
  • 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

    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
    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
    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.
    • 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.
    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

    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.
    Robert B. Ash
    Professor Emeritus, Mathematics
    Dept. of Mathematics
    University of Illinois
    1409 W Green St.
    Urbana, IL 61801

    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.

    12. Course Notes
    Lecture notes by ChingLi Chai, University of Pennsylvania.
    Course Notes
    Notes from some of my graduate courses, courtesy of Jeff Achter
    Reading Course Notes

    13. Robin Chapman
    Arithmetic (dvi, ps, pdf); Notes on Algebraic Numbers (dvi, ps, pdf); algebraic number theory (dvi, ps, pdf). Preprints Cubic identities for
    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:
    • 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.
    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 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.
    September 23 - October 2, 2002
    Lorentz Center
    , Leiden 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

    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).
    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

    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 &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.
    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
    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.
    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:

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