1. Algebraic Number Theory Archives Electronic preprint archives for mathematics research papers in algebraic number theory and arithmetic geometry. 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. Algebraic Number Theory - Wikipedia, The Free Encyclopedia algebraic number theory is a branch of number theory in which the concept of a number is expanded to the algebraic numbers which are roots of polynomials http://en.wikipedia.org/wiki/Algebraic_number_theory

Algebraic number theory From Wikipedia, the free encyclopedia Jump to: navigation search Algebraic number theory is a branch of number theory in which the concept of a number is expanded to the algebraic numbers which are roots of polynomials with rational coefficients. An algebraic number field is any finite (and therefore algebraic field extension of the rational numbers. These domains contain elements analogous to the integers , the so-called algebraic integers . In this setting, the familiar features of the integers (e.g. unique factorization ) need not hold. The virtue of the machinery employed — Galois theory group cohomology class field theory group representations and L-functions — is that it allows one to recover that order partly for this new class of numbers. edit See also Arithm©tique modulaire A survey of number theory, with applications (in French Wikipedia) List of algebraic number theory topics Algebraic number fields This number theory -related article is a stub . You can help Wikipedia by expanding it v d e Major topics in Number theory Algebraic number theory Analytic number theory Geometric number theory Computational number theory Numbers ... List of number theory topics Retrieved from " http://en.wikipedia.org/wiki/Algebraic_number_theory

3. MP473 2000 A course by Keith Matthews. Lecture notes (GIF slides), bibliography, web resources. http://www.numbertheory.org/courses/MP473/

MP473 Number Theory IIIH/IVH, Semester 2, 2000 Prepared by Keith Matthews Email: webmaster@numbertheory.org Web: http://www.numbertheory.org/keith.html 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 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; http://www.jmilne.org/math/CourseNotes/math676.html

Algebraic Number Theory pdf (current version 3.00) 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. v3.00; February 11, 2008; corrected; revisions and additions; 163 pages. 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 Errata pdf (old version 2.10)

5. 11: Number Theory algebraic number theory extends the concept of number to mean an element of some Local analysis usually arises as a part of algebraic number theory. http://www.math.niu.edu/~rusin/known-math/index/11-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 11: Number theory Introduction Number theory is one of the oldest branches of pure mathematics, and one of the largest. Of course, it concerns questions about numbers, usually meaning whole numbers or rational numbers (fractions). Elementary number theory involves divisibility among integers the division "algorithm", the Euclidean algorithm (and thus the existence of greatest common divisors), elementary properties of primes (the unique factorization theorem, the infinitude of primes), congruences (and the structure of the sets Z /n Z as commutative rings), including Fermat's little theorem and Euler's theorem extending it. But the term "elementary" is usually used in this setting only to mean that no advanced tools from other areas are used not The remaining parts of number theory are more or less closely allied with other branches of mathematics, and typically use tools from those areas. For example, many questions in number theory may be posed as Diophantine equations equations to be solved in integers without much preparation. Catalan's conjecture are 8 and 9 the only consecutive powers? asks for the solution to

6. 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

7. PlanetMath: Algebraic Number Theory This entry is a collection of links to entries on algebraic number theory in Planetmath (therefore bound to be always under construction). http://planetmath.org/encyclopedia/AlgebraicNumberTheory.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About algebraic number theory (Topic) I cannot retrieve this entry because the system is too busy. Please try again later. "algebraic number theory" is owned by alozano full author list view preamble View style: HTML with images page images TeX source See Also: norm and trace of algebraic number modular form Hecke operator bibliography for number theory ... Hecke algebra This object's parent Log in to rate this entry. view current ratings Cross-references: Hecke operators Hecke algebra modular form the arithmetic of elliptic curves ... PlanetMath There are 12 references to this entry. This is version 31 of algebraic number theory , born on 2005-03-15, modified 2007-04-08. Object id is , canonical name is AlgebraicNumberTheory Accessed 9229 times total.

8. Lecture Notes Of Advanced Courses Lecture notes by ChingLi Chai, University of Pennsylvania. http://www.math.upenn.edu/~chai/coursenotes.html

Lecture Notes of Advanced Courses 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)

9. Explicit Algebraic Number Theory Lorentz Center, Leiden, the Netherlands; 23 September 2 October 2002. 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.

10. A Brief Introduction To Classical And Adelic Algebraic Number Theory A Brief Introduction To Classical And Adelic algebraic number theory. William Stein. (based on books of SwinnertonDyer and Cassels). May 2004 http://modular.fas.harvard.edu/papers/ant/

A Brief Introduction To Classical And Adelic Algebraic Number Theory William Stein (based on books of Swinnerton-Dyer and Cassels) May 2004 Download for free: Online (HTML) version PDF version DVI version (0.6MB, missing 3 diagrams) PS version Latex source files License (this is basically the license this book is released under) I wrote this book for Math 129 at Harvard during Spring 2004. I'm making it available to everyone for free under very liberal conditions. For example, please feel free to put a copy on other web sites, or to make printouts or copies available to your students (even if you have to charge the students for reproduction costs).

11. Algebraic Number Theory - Number Theory Journals, Books & Online Media | Springe algebraic number theory Number Theory Combinatorics. From the review The present book has as its aim to resolve a discrepancy in the textbook http://www.springer.com/east/home/math/numbers?SGWID=5-10048-22-1414795-0

12. MIT OpenCourseWare | Mathematics | 18.786 Topics In Algebraic Number Theory, Spr This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers, Dirichlet s units theorem, http://ocw.mit.edu/OcwWeb/Mathematics/18-786Spring-2006/CourseHome/

skip to content Home Courses Donate ... Mathematics Topics in Algebraic Number Theory 18.786 Topics in Algebraic Number Theory Spring 2006 Some important properties of algebraic numbers follow from Minkowski's theorem: given a lattice in a Euclidean space, any bounded, convex, centrally symmetric region of large enough volume contains a nonzero lattice point. (Image courtesy of Jesus De Loera, Department of Mathematics, University of California, Davis.) Course Highlights This course features readings and assignments Course Description This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers, Dirichlet's units theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, basic analytic methods, and basic class field theory. An additional theme running throughout the course will be the use of computer algebra to investigate number-theoretic questions; this theme will appear primarily in the problem sets. Staff Instructor: Prof. Kiran Kedlaya

13. Algebraic Number Theory -- From Wolfram MathWorld algebraic number theory is the branch of number theory that deals with algebraic numbers. Historically, algebraic number theory developed as a set of tools http://mathworld.wolfram.com/AlgebraicNumberTheory.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Terr Algebraic Number Theory Algebraic number theory is the branch of number theory that deals with algebraic numbers . Historically, algebraic number theory developed as a set of tools for solving problems in elementary number theory , namely Diophantine equations (i.e., equations whose solutions are integers or rational numbers ). Using algebraic number theory, some of these equations can be solved by " lifting " from the field of rational numbers to an algebraic extension of More recently, algebraic number theory has developed into the abstract study of algebraic numbers and number fields themselves, as well as their properties. SEE ALSO: Algebraic Extension Algebraic Integer Algebraic Number Class Group ... Number Theory This entry contributed by David Terr REFERENCES: Stewart, I. and Tall, D. Algebraic Number Theory and Fermat's Last Theorem, 3rd ed. Wellesley, MA: A K Peters, 2000. CITE THIS AS: Terr, David . "Algebraic Number Theory." From MathWorld A Wolfram Web Resource, created by

14. Franz Lemmermeyer A standard course in algebraic number theory discusses the proofs of the main results on integral bases, discriminants, Dedekind rings, class groups, http://www.fen.bilkent.edu.tr/~franz/ant06.html

Algebraic Number Theory Schedule Mo 13:40 - 15:30, SAZ 02 We 15:40 - 17:30, SAZ 02 Motivation A standard course in algebraic number theory discusses the proofs of the main results on integral bases, discriminants, Dedekind rings, class groups, Dirichlet's unit theorem, etc. In this semester, I will instead concentrate on quadratic extensions of the rationals and of the rational function fields and introduce elliptic curves. This will allow us to do a lot of explicit calculations that cannot be done (by hand) for extensions of higher degree. Topics I. Quadratic Number Fields. Here we will discuss failure of unique factorization, ideal arithmetic, class number computation, and units. Applications: Bachet-Mordell equations y = x +k, some simple 3-descents on elliptic curves like x +y = Az , possibly the cubic reciprocity law. II. Quadratic Function Fields. These are quadratic extensions of the rational function fields F p [X]; their arithmetic has a lot in common with quadratic number fields. III. Arithmetic of Elliptic and Hyperelliptic Curves. These can essentially be identified with quadratic extensions of function fields.

15. GraNTS GRAduate Number Theory Seminar algebraic number theory and Elliptic Curves Ramblings on how elementary number theory motivates algebraic number theory, http://www.math.ucdavis.edu/~osserman/seminar/

GRAduate Number Theory Seminar: Algebraic Number Theory and Elliptic Curves If you are looking for the web page of last Spring's Kolyvagin seminar, you want here instead. Practical information Seminar description Lecture notes Lecture schedule ... References Practical Information Organizers: Alex Ghitza ( aghitza@math.mit.edu ) and Brian Osserman ( osserman@math.mit.edu When: Fall 2000, 2 hours/week, MoFr 11-12 Where: MIT, Rm 24-110 Seminar Description Format: a semester-long seminar giving a rapid introduction to algebraic number theory and elliptic curves. Hopefully, the material will end up including exactly what is needed for an elegant proof of the class number 1 problem for imaginary quadratic extensions, which we will then be able to present at the end of the semester. All participants will be expected to give lectures, and to prepare TeX lecture handouts. Topics: Dedekind domains, rings of integers, scheme-theoretic curves, finite morphisms thereof, splitting and ramification, the Tchebotarov density theorem and class field theory, selected introductory topics from elliptic curve theory, complex multiplication, modular curves, and the solution to Gauss' class number 1 problem. Prerequisites: A semester of graduate algebraic geometry, and familiarity with the commutative algebra required therein.

16. PARI/GP Development Headquarters PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves. http://pari.math.u-bordeaux.fr/

Main: PARI/GP? Download Search Support: FAQ Documentation Mailing Lists Links Development: Version Control Coding Guidelines Latest Changes Bugs ... Buildlogs Statistics: Benchmarks WWW Stats PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions. PARI is also available as a C library to allow for faster computations. Originally developed by Henri Cohen and his co-workers (Université Bordeaux I, France), PARI is now under the GPL and maintained by Karim Belabas with the help of many volunteer contributors. PARI is a C library, allowing fast computations. gp is an easy-to-use interactive shell giving access to the PARI functions. GP is the name of gp's scripting language. , the GP-to-C compiler, combines the best of both worlds by compiling GP scripts to the C language and transparently loading the resulting functions into gp. (gp2c-compiled scripts will typically run 3 or 4 times faster.) gp2c currently only understands a subset of the GP language. PARI/GP Development Last Modified: 2008-01-16 15:14:52 the PARI group

17. KANT Group (Algebra And Number Theory) Our name, KANT, is short for Computational algebraic number theory with a slight hint at its German origin (Immanuel Kant). KANT is also the name of a http://www.math.tu-berlin.de/~kant/

Institute of Mathematics KANT Group KANT Group (Algebra and Number Theory) About us Members Activities KANT/KASH ... E-mail About us We are the Algebra and Number Theory research group of the Institute of Mathematics at Our name, KANT , is short for C omputational A lgebraic N umber T heory with a slight hint at its German origin ( Immanuel Kant ). KANT is also the name of a sophisticated computer algebra system that has been developed under the project leadership of Prof. Dr. M. E. Pohst more about KANT We are furthermore involved in the research projects SCIEnce QaoS , and GiANT Members Prof. Dr. M. E. Pohst Prof. Dr. F. Hess Oliver Voigt (System Administrator) Dr. Claus Fieker ... Dr. Sebastian Pauli PhD Students Thorsten Lagemann Jose Mendez Moritz Minzlaff Osmanbey Uzunkol ... Marcus Wagner Diplomanden Sebastian Freundt Aneesh Karve Full list of members Activities ANTS VII The 7th Algorithmic Number Theory Symposium will take place from July 23 to July 28, 2006 at Technische Universität Berlin. ( more Lange Nacht der Wissenschaften 2006: KryptoLabor Wir waren wieder bei der Langen Nacht der Wissenschaften am 13. Mai 2006 mit dem

18. Mastermath The course provides a thorough introduction to algebraic number theory. It treats the arithmetic of the number rings that occur in (algorithmic) practice. http://www.mastermath.nl/program/00003/00009/

About Mastermath Registration Links Locations ... Spring 2009 Algebraic Number Theory Credits 8 credit points Instructors Top, J. (Rijksuniversiteit Groningen), Smit, B. de (Universiteit Leiden) E-mail J.Top@math.rug.nl desmit@math.leidenuniv.nl Description The course provides a thorough introduction to algebraic number theory. It treats the arithmetic of the number rings that occur in (algorithmic) practice. Topics: Introduction to algebraic numbers and number rings. Ideal factorization, finiteness results on class groups and units, explicit computation of these invariants. Special topic: the number field sieve. Each week, students have to hand in 4 exercises from the course notes out of those listed on the website of this course. Solving the more difficult problems will result in a higher grade. The final problem set of the course will be more substantial. Organization Mondays from September 11 - December 18, 2006, 10:15 - 13:00. The final hour (12:15-13:00) will be devoted to homework problems. Examination The final grade is exclusively based on the results obtained for the weekly homework assignments. The last problem set will be more substantial and determine one third of the final grade. Literature We will use the course notes and homework exercises Prerequisites Undergraduate algebra, i.e., the basic properties of groups, rings and fields. This material is covered in first and second year algebra courses in the bachelor program of most universities. The course notes

19. Algebraic Number Theory And Related Topics algebraic number theory and Related Topics at RIMS, December 11 15, 2006 Organizer Ki-ichiro Hashimoto (Waseda Univ.) http://www.math.waseda.ac.jp/NTseminar/RIMS2006-e.html

20. The Math Forum - Math Library - Algebraic Num. Th. A short article designed to provide an introduction to algebraic number theory. Subcategories include rings of algebraic integers, quadratic extensions, http://mathforum.org/library/topics/alg_nt/

Browse and Search the Library Home Math Topics Number Theory : Algebraic Num. Th. Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Algebraic Number Theory: Global Fields - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to algebraic number theory. Subcategories include rings of algebraic integers, quadratic extensions, Iwasawa theory, Galois theory, Langlands-Weil conjectures, density theorems, Adele rings and groups, class groups and Picard groups of orders, and many more. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> All Sites - 24 items found, showing 1 to 24 Algebraic Number Theory Archives - Boston, Grayson Preprints about algebraic number theory and arithmetic geometry are accepted in electronic form for storage until publication. There are instructions for authors who wish to submit preprints to the archives and for for joining the mailing list (members ...more>> Algebra Through Problem Solving - Hillman, Alexanderson

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