21. Introductory Algebraic Number Theory - Cambridge University Press algebraic number theory is a subject which came into being through the attempts of mathematicians to try to prove Fermat s last theorem and which now has a http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521540119

22. Math 248B - Algebraic Number Theory - Winter 2004 We conclude by discussing automorphic forms in general and their role in solving fundamental questions in algebraic number theory. It will be sweet. http://math.stanford.edu/~brubaker/math248b.html

Math 248B - Algebraic Number Theory - Winter 2004 General information Syllabus Homework Handouts General information Meeting Time Mon., Wed., Fri., 10:00 - 10:50 (may be negotiated otherwise) Location Building 380 (Math), room 381-T Professor Ben Brubaker ( brubaker@math.stanford.edu Office: 382-F (2nd floor, Math building 380) Office Phone: 3-4507 Office Hours: Monday 2-3:30, Wednesday 2-3:30, or by appointment. Course Assistant Ryan Vinroot ( vinroot@math.stanford.edu Office: 380-G (Basement, Math building) Office hours: By appointment only. Textbooks Multiplicative Number Theory , by Harold Davenport. The Theory of the Riemann Zeta Function , by E.C. Titchmarsh. Course Content We will review the basics of class field theory in the first week through the lens of reciprocity. Then we'll head to Davenport, covering the first 8 chapters, essential and classical analytic number theory from which all else follows. We'll break and do several weeks on the zeta function. Classical stuff again, but often shoved under the rug. We'll end with a potpourri of topics, including Siegel's theorem and proofs of algebraic facts using analytic information. We conclude by discussing automorphic forms in general and their role in solving fundamental questions in algebraic number theory. It will be sweet. Prerequisites There are essentially no prerequisites for this course. If you took Rubin's 248A in the fall, or know the equivalent information, you'll have a better view from which to understand the arc of the course, but its not at all necessary in understanding the day to day material.

23. NoMaDS: Main Page North of England algebraic number theory Group, meeting termly, based at Durham, Nottingham, Sheffield and Manchester. Fifteenth meeting Nottingham http://www.afjarvis.staff.shef.ac.uk/lms/

North of England Algebraic Number Theory Group This is the home page for the North of England Algebraic Number Theory Group. This group is based at Durham, Nottingham, Sheffield and Manchester, and we are grateful to the London Mathematical Society for financially supporting the group by means of a Scheme 3 grant. This grant has been renewed for 2006-07, and pays for travel expenses for NoMaDS members, as well as other visitors (if sufficient funds are available). Although our official title is the one given above, we informally refer to ourselves as NoMaDS (an abbreviation of No ttingham, Ma nchester, D urham and S heffield, the host cities), as suggested by John Cremona. Nineteenth meeting, Sheffield (8/3/2007) The nineteenth meeting takes place on Thursday March 8th in Sheffield. Here is the programme: Paul Buckingham (Sheffield) The canonical fractional Galois ideal at s=0 coffee/tea David Sim (Nottingham) Dimensions of spaces of higher order cusp forms tea/coffee Ambrus Pal (Imperial) Drinfeld modular curves and the arithmetic of elliptic curves defined over function fields The talks will take place in and (coffee), Hicks Building, Sheffield.

24. Notes For Dick Gross' Algebraic Number Theory Course As many of you know, I have been typing up the notes for the Number Theory Course being taught by Dick Gross who is visiting from Harvard during the Spring http://www.math.utah.edu/~sather/notes.html

Notes for Dick Gross' Algebraic Number Theory Course Spring 1999 As many of you know, I have been typing up the notes for the Number Theory Course being taught by Dick Gross who is visiting from Harvard during the Spring Semester of 1999. 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 . Cheers. Sean Lectures 1-4 .ps or .pdf : material from 14 January to 26 January Lectures 5-8 .ps or .pdf : material from 28 January to 9 February Lectures 9-12 .ps or .pdf : material from 2 February to 25 February Lectures 13-16 .ps or .pdf : material from 2 March to 11 March Lectures 17-18 .ps or .pdf : material from 23 March to 25 March Lectures 1-18 .ps or .pdf : material from 14 January to 25 March Lectures 1-18 compressed .ps.gz or .pdf.gz : material from 14 January to 25 March Last updated 5.25.99

25. Magic Squares And Algebraic Number Theory « Abstract Nonsense Ew. I didn’t learn algebraic number theory from a single book; each book had different strengths and weaknesses, so whenever I hit a weak point, http://abstractnonsense.wordpress.com/2007/03/09/magic-squares-and-algebraic-num

var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E")); Abstract Nonsense Mathematics, liberal politics, and rants about the news of the day Home About me Contact Me Magic Squares and Algebraic Number Theory ... magic square a b c d e f g q h ^2]; we want to have, for example, a h e This alone is very restrictive, since it requires ( a e h ^2) to be an arithmetic sequence, a sufficiently special situation that unless a e h a h e First, the easy part: we can assume a e , and h are coprime; otherwise, divide by their greatest common divisor. If e is even, then 2 e a and h to be odd since odd squares are equivalent to 1 mod 8, so that a and h are even and the three numbers are not coprime. So e a and h Now, when we have sums of two squares, the most natural environment to study divisibility is Z i ], the ring of Gaussian integers. We get ( a hi a hi e ^2. As a and h are odd, a hi is not divisible by 2, so both a hi and a hi must be divisible by 1 + i a hi i a hi i a h i h a )/2, and similarly (

26. A K Peters, Ltd. - Algebraic Number Theory And Fermat’s Last Theorem “The book remains, as before, an extremely attractive introduction to algebraic number theory, from the idealtheoretic perspective.” Recommendations http://www.akpeters.com/product.asp?ProdCode=1195

27. Algebraic Number Theory And Related Topics algebraic number theory and Related Topics at RIMS, December 10 14, 2007 Organizers Mamoru Asada (Kyoto Institute of Technology) http://hiro2.pm.tokushima-u.ac.jp/RIMS2007-e.html

Algebraic Number Theory and Related Topics" at RIMS, December 10 - 14, 2007 Organizers: Mamoru Asada (Kyoto Institute of Technology) Hiroaki Nakamura (Okayama University) pdf file Japanese Banquet : December 12 (Wed) 18:00-20:00 at COOP "Hokuto" December 10 (Mon) Akio Tamagawa (Kyoto University, RIMS) Torsion of abelian schemes and rational points on moduli spaces (joint work with Anna Cadoret) Shinya Harada (Kyushu University) Smallness of fundamental groups for arithmetic schemes (joint work with Toshiro Hiranouchi) Kentaro Nakamura (University of Tokyo) Classification of two dimensional trianguline representations Kenichi Bannai (Nagoya University) $p$-adic elliptic polylogarithm and the two-variable $p$-adic $L$-function for CM elliptic curves Tomoyuki Abe (University of Tokyo) Comparison between Swan conductors and characteristic cycles December 11 (Tue) Yoichi Mieda (University of Tokyo) Cycle classes, Lefschetz trace formula and integrality for $p$-adic cohomology

28. Lecture Notes Lecture notes on algebraic number theory by J.S. Milne (dvi, ps, pdf; E), L. Merel (dvi, FR), D. Gross (ps, pdf; E), Wolfgang Ruppert (ps.gz, D), http://www.rzuser.uni-heidelberg.de/~hb3/notes.html

Lecture Notes Abelian Varieties Lecture notes on Abelian Varieties by J.S. Milne (dvi, ps, pdf; E), Bas Edixhoven (ps.gz, FR), Wolfgang Ruppert (ps.gz, D), Polishchuk Lecture notes on Jacobian Varieties by Bas Edixhoven (ps.gz, FR), Explicit approaches to modular Abelian varieties; thesis by W. Stein (tex, dvi, ps; E) Algebra Lecture Notes by Bas Edixhoven (tex, ps, ps.gz, FR), Paul Garrett (ps, E; also as pdf B. Külshammer (dvi, D), Lee Lady (dvi, ps; E), Schwaenzl (ps.gz, D), Spindler (ps.gz, D) Lecture notes by Karl Mathiak: Introduction (ps, D), Algebra (ps, D), valuations (ps, D), Krull valuations (ps, D), real valuations (ps, D), Algebra for computer scientists (ps, D), computer algebra (pdf, D). Lecture Notes on rings by B. Külshammer (dvi, D) Algebraic Geometry Lecture notes on Algebraic Geometry by J.S. Milne (dvi, ps, pdf; E), Antoine Chambert-Loir (ps.gz, FR, also as pdf M. Flach G. Harder (dvi, D; also as ps ); parts of this huge file will appear as a book: here are the

29. Foundations And Trends In Communications And Information Theory algebraic number theory and Code Design for Rayleigh Fading Channels algebraic number theory is having an increasing impact in code design for many http://www.nowpublishers.com/product.aspx?product=CIT&doi=0100000003

30. Algebraic Number Theory This leads to understanding that number theory and algebraic geometry is in fact one and the same domain. The core of number theory being an elementary http://www.mccme.ru/mathinmoscow/courses/view.php?name=Algebraic Number Theory.h

31. Springer Online Reference Works algebraic number theory. The branch of number theory with the basic aim of These are four main problems in algebraic number theory, and answering them http://eom.springer.de/A/a011600.htm

Encyclopaedia of Mathematics A Article referred from Article refers to Algebraic number theory The branch of number theory with the basic aim of studying properties of algebraic integers in algebraic number fields of finite degree over the field of rational numbers (cf. Algebraic number The set of algebraic integers of a field of of degree (cf. Extension of a field ; this means that each algebraic integer (i.e. element of ) can be written in the form where all the run through the rational integers (i.e. ). Moreover, such a representation is unique for each algebraic integer in However, properties of rational integers often do not have obvious analogues for algebraic integers. The first such property is related to units, the invertible elements of (cf. Unit ). The field of rational numbers has only and as units, but a general algebraic number field may contain an infinite number of units. E.g. consider the real quadratic field , where is a rational integer not equal to a square. If, moreover, , then is an integral basis for it. The

32. UM Mathematics: Number Theory The department has long maintained a vigorous graduate program in number theory. Faculty. Permanent. B. Conrad. algebraic number theory; arithmetic http://www.math.lsa.umich.edu/research/number_theory/

Home People Graduate Program Undergraduate Program ... Links Search Mathematics Search WWW Graduate Program in Number Theory at the University of Michigan The department has long maintained a vigorous graduate program in number theory. Faculty Permanent: B. Conrad Algebraic number theory; arithmetic geometry. K. Soundararajan Analytic number theory, distribution of prime numbers H.L. Montgomery Analytic number theory, distribution of prime numbers, Fourier analysis, analytic inequalities, probability. C. Skinner Algebraic number theory;arithmetic of L-values. T. Wooley Analytic number theory, diophantine equations. Faculty in related areas include: I. Dolgachev (algebraic geometry), W. Fulton (algebraic geometry), R. Lazarsfeld (algebraic geometry), S. DeBacker (representation theory), G. Prasad (arithmetic of algebraic groups).

33. Algebraic Number Theory - Wolfram Mathematica With its convenient symbolic representation of algebraic numbers, Mathematica s stateof-the-art algebraic number theory capabilities provide a concrete http://reference.wolfram.com/mathematica/guide/AlgebraicNumberTheory.html

baselang='AlgebraicNumberTheory.en'; PreloadImages('/common/images2003/link_products_on.gif','/common/images2003/link_purchasing_on.gif','/common/images2003/link_forusers_on.gif','/common/images2003/link_aboutus_on.gif','/common/images2003/link_oursites_on.gif'); DOCUMENTATION CENTER SEARCH Mathematica Mathematics and Algorithms Number Theory Mathematica ... Number Theoretic Functions Algebraic Number Theory With its convenient symbolic representation of algebraic numbers, Mathematica Mathematica 's powerful unified environment. AlgebraicNumber algebraic number represented in a particular field MinimalPolynomial AlgebraicNumberPolynomial AlgebraicIntegerQ AlgebraicUnitQ ... ToNumberField find a common field, or express numbers in a given field NumberFieldIntegralBasis NumberFieldClassNumber NumberFieldDiscriminant NumberFieldRegulator ... Extension field extension for number theoretic and polynomial operations RootReduce reduce an algebraic number to minimal Root form ToRadicals convert to explicit radicals TUTORIALS Algebraic Numbers Algebraic Number Fields MORE ABOUT Algebraic Numbers Number Theory Number Theoretic Functions RELATED LINKS Demonstrations related to Algebraic Number Theory The Wolfram Demonstrations Project Ask a question about this page Suggest an improvement ... Leave a message for the team

34. UR Math Algebra And Number Theory Group apizermath, algebraic number theory, arithmetic of quaternion algebras and its connections to modular forms, Brandt matrices, Hecke operators, and Ramanujan http://math.rochester.edu/research/algebra_and_number_theory

35. FreeScience - Books - Algebraic Number Theory This is a summary of the 1999–2000 course on algebraic number theory. Proofs will generally be sketched rather than presented in detail. http://www.freescience.info/books.php?id=349

36. Ant07 - William Stein's Wiki algebraic number theory 2007 Math 581F. A graduate course at University of Washington taught by William Stein (undergraduates are welcome). http://wiki.wstein.org/ant07

Search: Login RecentChanges FindPage HelpContents Immutable Page Info Attachments More Actions: Raw Text Print View Render as Docbook Delete Cache Check Spelling Like Pages Local Site Map Rename Page Delete Page My Pages Subscribe User Remove Spam Package Pages Algebraic Number Theory 2007: Math 581F A graduate course at University of Washington taught by William Stein (undergraduates are welcome). Monday, Wednesday and Friday at 2:30pm in PDL C036 Office Hours: Tuesday and Thursday 2-3pm Final Projects Lecture schedule overview Lecture plan (more detailed) Video of lectures ... Student list ant07 (last edited 2007-12-07 21:41:59 by was Immutable Page Info Attachments More Actions: Raw Text Print View Render as Docbook Delete Cache Check Spelling Like Pages Local Site Map Rename Page Delete Page My Pages Subscribe User Remove Spam Package Pages MoinMoin Powered Python Powered Valid HTML 4.01

37. Intute Science, Engineering And Technology - Full Record Details For Algebraic N , This resource gives access to lecture notes for a course on algebraic number theory held at the University of Exeter. These notes were prepared...... http://www.intute.ac.uk/sciences/cgi-bin/fullrecord.pl?handle=20080105-17395680

38. Algebraic Number Theory (LTCC) This course gives a nontechnical introduction to some important topics in algebraic number theory. After introducing the basic objects (algebraic integers, http://www.mth.kcl.ac.uk/staff/m_breuning/ltcc/

Algebraic Number Theory For PhD students at the London Taught Course Centre This course gives a non-technical introduction to some important topics in algebraic number theory. After introducing the basic objects (algebraic integers, ideals and ideal class groups, units) we will discuss p-adic numbers and local-global principles, zeta functions and class number formulas, and cyclotomic fields. Lectures: Time: Mondays 10.30-12.30, 21 January 2008 to 18 February 2008 Location: De Morgan House, Russell Square Lecturer: Dr Manuel Breuning , King's College London Course structure and course materials: Date Topics Lecture notes Problem sheets 21 January 2008 algebraic extensions, algebraic integers, ideals, ideal class groups, units Lecture notes, Part 1 Problem sheet 1 28 January 2008 Lecture notes, Part 2 4 February 2008 Zeta functions, class number formulas Lecture notes, Part 3 Problem sheet 2 11 February 2008 Cyclotomic fields Lecture notes, Part 4 18 February 2008 p -adic numbers Lecture notes, Part 5 Books: The course will not follow one particular book, but there are many books which are useful as an introduction to some of the material of the course and for further reading, for example the books in the following list. Algebraic number theory , CUP, 1991.

39. B9b: Algebraic Number Theory | Mathematical Institute - University Of Oxford An introduction to algebraic number theory. The aim is to describe the properties of number fields, but particular emphasis in examples will be placed on http://www.maths.ox.ac.uk/courses/[catpath]-0

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40. Andrew Granville -- Publications In Algebraic Number Theory Andrew Granville s publications in algebraic number theory. By subject Analytic, Algebraic, Algorithmic, and Combinatorial number theory, other research, http://www.dms.umontreal.ca/~andrew/Algebraic.html

Publications by year: Preprints Andrew Granville 's publications in algebraic number theory By subject: Analytic Algebraic Algorithmic , and Combinatorial number theory, other research , and expository writing. Topics: Applications of Faltings' Theorem, Generalized Fermat equations, Class number of cyclotomic fields, the abc-conjecture, Finite fields, Elliptic Curves, and Fermat's Last Theorem. Applications of Faltings' Theorem with Enrico Bombieri and Janos Pintz Article and AMS Review Squares in arithmetic progressions Duke Mathematical Journal, vol. (1992) pages 165-204 with Henri Darmon Article and AMS Review On the equations z m =F(x,y) and Ax p +By q =Cz r Bulletin on the London Mathematical Society, (1995) pages 515-543 Article and AMS Review The set of exponents, for which Fermat's Last Theorem is true, has density one , vol (1985) pages 55-60 Generalized Fermat equations with Henri Darmon Article and AMS Review On the equations z m =F(x,y) and Ax

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