1. Algebraic Number Theory Archives Large linked preprint archives for papers in algebraic number theory and Arithmetic Geometry.Category Science Math Number Theory Publications Preprint Archives......Electronic preprint archives for mathematics research papers in algebraicnumber 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. NUMBER THEORY WEB (AMERICAN SITE) Alebraic number theory course at the University of Exeter gives a background on rings and ideals as well as problem sheets and course notes available for download. MAS4002 algebraic number theory. This is the home page for the algebraic number theory course. At present it is still http://www.math.uga.edu/~ntheory/web.html

Number Theory Web (American Site) Aims New Listings Number theorists' Home Pages/Departmental listings Things of Interest to Number Theorists ... Search the Number Theory Web Pages in Athens, Georgia This site is a mirror of the Australian site at University of Queensland, Brisbane, Australia The Italian mirror site The British mirror site is at University of Cambridge The Japanese mirror site is at University of Electro-Communication, Tokyo The Indian mirror site is at the Harish-Chandra Research Institute, Allahabad (courtesy of Shripad Garge Created and maintained by Keith Matthews , Dept of Math, University of Queensland, Brisbane, Australia Suggestions for additions or improvements are welcome Email: krm@maths.uq.edu.au Last modified 19th December 2002

3. MP473 2000 (G L) Cassels, Frohlich algebraic number theory 3. (G L) Golstein Analytic Number Theory (Chapters 16) 4. 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 - Cambridge University Press a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced http://books.cambridge.org/0521438349.htm

Home Catalogue Related Areas: Pure Mathematics Cambridge Studies in Advanced Mathematics New titles Email For updates on new titles in: Pure Mathematics Algebraic Number Theory A. Fröhlich, M. J. Taylor Hardback In stock Reviews ‘It promises to become a classic.’Monatshefte für Mathematik ‘ very nice and carefully written many excellent exercises ’European Mathematical Society Newsletter Contents Notation; Introduction; 1. Algebraic foundations; 2. Dedekind domains; 3. Extensions; 4. Classgroups and units; 5. Fields of low degree; 6. Cyclotomic fields; 7. Diophantine equations; 8. L-functions; Appendices; Exercises; Glossary of theorems; Index. Cambridge University Press 2001. Security Order by phone (+44 (0)1223 326050) or fax (+44 (0)1223 326111).

5. Notes For Dick Gross' Algebraic Number Theory Course, University Of Utah Taken by Sean SatherWagstaff, Utah, Spring 1999. In PS and PDF formats.Category Science Math Number Theory Algebraic......Notes for Dick Gross' algebraic number theory Course University ofUtah. Spring 1999. During the Spring Semester of 1999, I typed 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

6. Algebraic Number Theory Course notes by Robin Chapman, University of Exeter, May 2000.Category Science Math Number Theory Algebraic......MAS4002 algebraic number theory. This is the home page for the AlgebraicNumber Theory course. At present it is still under construction. 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. Algebraic Number Theory: Next Global Theory Up Number Theory Previous Analytic Number Theory algebraic number theory http://hilbert.dartmouth.edu/graduate-students/syllabi/graduate-syllabi/number-t

Next: Global Theory: Up: Number Theory Previous: Analytic Number Theory: Algebraic Number Theory: Global Theory: Local Theory: root

8. Online Number Theory Lecture Notes theory (Nigel Byott); MAS4002 algebraic number theory, Course notesby Robin Chapman, University of Exeter; Lectures on irregularities http://www.math.uga.edu/~ntheory/lecture_notes.html

Online number theory lecture notes Selected from N4.html Lecture notes in Greek (Jannis Antoniadis) Number theory in the 17th and 18th centuries (ps 1281K) Elliptic curves (Mordell's theorem) (ps 1021K) L-series (ps 1953K) Lecture notes on p-adic numbers and introductory number theory (Andrew Baker) Zahlentheorie (Notes by Winfried Bruns) Lecture notes on elementary number theory (Nigel Byott) MAS4002: Algebraic Number Theory , Course notes by Robin Chapman, University of Exeter Lectures on irregularities of point distribution , (notes by William Chen) Elementary and Analytic Number Theory , Lecture notes by William Chen Computational class field theory , A course given at the Middle East Technical University, Ankara, 1997 by Henri Cohen (dvi 255K) Draft chapters of elliptic curve handbook ECH1 Lecture notes on elementary number theory (John Cremona) Modular forms (Igor Dolgachev) The Modular curves X (N), Lecture notes by Bas Edixhoven Lecture notes for Math 259 : Introduction to Analytic Number Theory (Spring 1998) (Noam Elkies) Course notes for analytic number theory (Graham Everest) (ps 442K) Course Notes for elementary and algebraic number theory , Ivan Fesenko Math 780: Elementary Number Theory , Notes by Michael Filaseta, 1997 Vinogradov's three-primes theorem , notes by Timothy Gowers (dvi 54K) Notes on sieve theory (Ben Green) Lecture notes on algebraic number theory (Jerome Hoffman) Lecture notes on elementary number theory (Bruce Ikenaga) , Lecture notes by Franz Lemmermeyer Elliptische Kurven , Lecture notes by Franz Lemmermeyer

9. Courses Course Notes by Ivan Fesenko, University of Nottingham. PS, PDF.Category Science Math Number Theory Education...... extensions. Introduction to algebraic number theory ps file (432K);Introduction to algebraic number theory - pdf file (193K) This 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 modules over rings, Noetherian modules, unique factorization domains and polynomial rings over them, modules over principal ideal domains; spectrum of rings and their interpretations, localization; field extensions. 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.

10. The Math Forum - Math Library - Algebraic Num. Th. The Math Forum's Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites relating to algebraic number theory. algebraic number theory Global Fields Dave Rusin; The Mathematical Atlas http://mathforum.com/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

11. Explicit Algebraic Number Theory Lorentz Center, Leiden, the Netherlands; 23 September 2 October 2002.Category Science Math Number Theory Events Past Events...... Subject. The title Explicit algebraic number theory is borrowed from theseries 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.

12. NWO-OTKA--Stieltjesweek Explicit Algebraic Number Theory NWOOTKA-Stieltjesweek Explicit algebraic number theory. Start theNWO-OTKA workshop on Explicit algebraic number theory. Schedule. http://www.math.leidenuniv.nl/~psh/EANT/stweek.shtml

NWO-OTKA-Stieltjesweek Explicit algebraic number theory Start: Monday September 23, 10.00am: arrival of participants, coffee Location: Lorentz Center (Oort building, third floor). End: Friday September 27, 4.30pm: closing reception with drinks Location: Lorentz Center Speakers Courses on Monday through Thursday will be given by Hendrik Lenstra hwl@math.leidenuniv.nl Peter Stevenhagen psh@math.leidenuniv.nl with guest appearances on Wednesday by schoof@mat.uniroma2.it Bart de Smit desmit@math.leidenuniv.nl The Friday concluding the Stieltjesweek is the first day of the NWO-OTKA workshop on Explicit algebraic number theory. Schedule On Monday through Thursday we have the following day schedule: 10.30-11.30: lecture 1 11.50-12.50: lecture 2 12.50-13.45: lunch 13.45-15.30: homework 15.30-16.00: tea 16.00-17.00: problem session Proposed lectures: 1. Profinite groups (Lenstra) 2. Class field theory (Stevenhagen) 3. The Chebotarev density theorem (Lenstra) 4. Kummer theory (Stevenhagen) 5. Infrastructure (Schoof) 6. Radical Galois groups (de Smit)

13. ALGEBRAIC-NUMBER-THEORY@LISTSERV.UIUC.EDU LSoft, ALGEBRAIC-NUMBER-THEORY@LISTSERV.UIUC.EDU. algebraic number theory.List name ALGEBRAIC-NUMBER-THEORY. SUBSCRIBE ALGEBRAIC-NUMBER-THEORY. http://www.lsoft.com/scripts/wl.exe?SL1=ALGEBRAIC-NUMBER-THEORY&H=LISTSERV.UIUC.

14. The Math Forum - Math Library - Algebraic Num. Th. This page contains sites relating to algebraic number theory. Browse and Searchthe Library Home Math Topics Number Theory Algebraic Num. Th. 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

15. About "Algebraic Number Theory Archives" algebraic number theory Archives. Library Help Visit this site http//www.math.uiuc.edu/AlgebraicNumber-Theory/.Author Boston, Grayson. http://mathforum.org/library/view/2516.html

Algebraic Number Theory Archives Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.math.uiuc.edu/Algebraic-Number-Theory/ Author: Boston, Grayson Description: 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 of the mailing list receive announcements of preprints when they are deposited in the archives), and a search service that allows you to search an index of online mathematical works by keyword. The index includes the preprints automatically. Levels: College Research Languages: English Resource Types: Preprints Math Topics: Algebraic Geometry Algebraic Number Theory Suggestion Box Home ... Search http://mathforum.org/ webmaster@mathforum.org

16. 11R: Algebraic Number Theory: Global Fields 11R algebraic number theory global fields. Introduction. Textbooks, referenceworks, and tutorials. There are quite a few texts in algebraic number theory. 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

17. 11S Algebraic Number Theory: Local And P-adic Fields 11S algebraic number theory local and padic fields. Introduction. We usethis page mostly to store information about p-adic numbers. History. http://www.math.niu.edu/~rusin/known-math/index/11SXX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 11S Algebraic number theory: local and p-adic fields Introduction We use this page mostly to store information about p-adic numbers. History Applications and related fields The p-adics are formed by completing the rationals with respect to various non-archimedean metrics; thus the material on metric spaces is likely to be relevant. Subfields Polynomials Ramification and extension theory Galois theory Integral representations Galois cohomology, See also 12Gxx, 16H05 Class field theory; p-adic formal groups, See also 14L05 Langlands-Weil conjectures, nonabelian class field theory, See also 11Fxx, 22E50 Zeta functions and L -functions, See also 11M41, 19F27 Algebras and orders, and their zeta functions, See also 11R52, 11R54, 16H05, 16Kxx K-theory of local fields, See also 19Fxx Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.) Other nonanalytic theory Prehomogeneous vector spaces [new in 2000] None of the above but in this section Parent field: 11: Number Theory Browse all (old) classifications for this area at the AMS.

18. LMS/EPSRC Short Courses An LMS/EPSRC Short Course. King's College, London, UK; 26 September 2002.Category Science Math Number Theory Events Past Events......LMS/EPSRC Short Course on Topics in algebraic number theory. King’sCollege London, 26 September 2002 Organiser David Burns. Algebraic http://www.lms.ac.uk/activities/research_meet_com/short_course/11_app.html

19. Instructional Conference On Algebraic Number Theory HarishChandra Research Institute, Allahabad, India; 825 November 2000.Category Science Math Number Theory Events Past Events...... Advanced Instructional Workshop on algebraic number theory (withspecial reference to Elliptic Curves) (November 8 25, 2000). http://www.mri.ernet.in/~mathweb/numbertheory2000/

HRI Main Page Mathematics Advanced Instructional Workshop on Algebraic Number Theory (with special reference to Elliptic Curves) (November 8 25, 2000) This workshop will be followed by an International Conference on Number Theory from November 26 to November 29, 2000. Useful Links: Topics to be covered Weekly Schedule List of Speakers Local Coordinators: Dr. S. D. Adhikari. Cabin No. 3, Phone No. (O) 2017, (R) 4017 e-mail: Dr. B. Ramakrishnan Cabin No. 6, Phone No. (O) 2019, (R) 4019 e-mail: Organizing Committee HRI Math Page HRI Main Page Last modified: Sun Nov 5 03:01:50 IST 2000 by Shripad

20. Algebraic Number Theory Archive Eprint archive for research in algebraic number theory and arithmeticgeometry. algebraic number theory Archive. Welcome to the 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. Instructions for joining the mailing list . Members of the mailing list receive announcements of new e-prints. Some TeX fonts in compressed tar format, including the lams* and xy* fonts, which are needed for some of the e-prints. Papers math.NT/0303026 : 3 Mar 2003, Existence de F-cristaux avec structures supplementaires , by Jean-Pierre Wintenberger. math.NT/0303001 : 28 Feb 2003, Non-isogenous superelliptic jacobians , by Yuri G. Zarhin. math.NT/0302319

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