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Two meetings of the AMS in the fall of 1989---one at the Stevens Institute of Technology and the other at Ball State University---included Special Sessions on the role of $p$-adic methods in number theory and algebraic geometry. This volume grew out of these Special Sessions. Drawn from a wide area of mathematics, the articles presented here provide an excellent sampling of the broad range of trends and applications in $p$-adic methods. ... Read more

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Peter Swinnerton-Dyer's mathematical career encompasses more than 60 years' work of amazing creativity. This volume, dedicated to him on the occasion of his 75th birthday, provides contemporary insight into several subjects in which his influence has been notable. The contributions come from leading researchers in analytic and arithmetic number theory, and algebraic geometry. Topics treated include rational points on algebraic varieties, the Hasse principle, Shafarevich-Tate groups of elliptic curves and motives, Zagier's conjectures, descent and zero-cycles, Diophantine approximation, and Abelian and Fano varieties. ... Read more

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One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups.

These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld's own interests in algebra, algebraic geometry, and number theory.

Contributors: A. Eskin, V.V. Fock, E. Frenkel, D. Gaitsgory, V. Ginzburg, A.B. Goncharov, E. Hrushovski, Y. Ihara, D. Kazhdan, M. Kisin, I. Krichever, G. Laumon, Yu.I. Manin, A. Okounkov, V. Schechtman, and M.A. Tsfasman.

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Chapters: Quadratic Reciprocity. Source: Wikipedia. Pages: 427. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic which gives conditions for the solvability of quadratic equations modulo prime numbers. There are a number of equivalent statements of the theorem, which consists of two "supplements" and the reciprocity law: Let p, q ... Read more

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Presents 18 research papers on algebraic geometry, algebraic number theory and algebraic groups. Two summarized surveys on Arthur's invariant trace formula and the representation theory of quantum linear groups by K.F. Lai and Jian-Pan Wang respectively are included. ... Read more

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This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples. It is the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.

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vi+139 pp. The author presents a concise introduction to algebraic number theory suitable for a beginning graduate course. The book is based on lectures given at the University of Salzburg and Brigham Young University. Many exercises are incorporated into the text. As for prerequisites, the reader should be familiar with linear algebra, and some basic abstract algebra including Galois theory. The methods used are classical, along the lines of the work of Dedekind and Hilbert. The Minkowski geometry of numbers is developed and used as a tool. The author takes pains to show how modern commutative algebra and algebraic geometry originate in the subject matter of algebraic number theory. Students who decide to specialize in algebraic number theory will find the suggestions for further reading helpful.Algebraic number theory is one of the great accomplishments of pure mathematics. This was the view of David Hilbert and Hermann Weyl, for example. This brief introduction conveys the power and elegance of the subject, and tempts the reader to delve further into the literature. Chapter headings: 1. Basic Concepts. 2. Arithmetic in relative extensions. 3. Geometry of numbers. 4. Analytic methods. 5. Arithmetic in Galois extensions. 6. Cyclotomic fields. 7. The Kronecker- Weber theorem. 8. Zeta functions and Riemann hypothesis.Not available for international shipping through yahoo.com. Contact kendrickpress.com to purchase this book internationally. ... Read more

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Algebraic Number Field. Field extension, Field (mathematics), Algebraic number theory, Rational number, Vector space, Dirichlet's unit theorem, Modulus (algebraic number theory), Chebotarev's density theorem ... Read more

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Webster's bibliographic and event-based timelines are comprehensive in scope, covering virtually all topics, geographic locations and people. They do so from a linguistic point of view, and in the case of this book, the focus is on "Algebraic Number Theory," including when used in literature (e.g. all authors that might have Algebraic Number Theory in their name). As such, this book represents the largest compilation of timeline events associated with Algebraic Number Theory when it is used in proper noun form. Webster's timelines cover bibliographic citations, patented inventions, as well as non-conventional and alternative meanings which capture ambiguities in usage. These furthermore cover all parts of speech (possessive, institutional usage, geographic usage) and contexts, including pop culture, the arts, social sciences (linguistics, history, geography, economics, sociology, political science), business, computer science, literature, law, medicine, psychology, mathematics, chemistry, physics, biology and other physical sciences. This "data dump" results in a comprehensive set of entries for a bibliographic and/or event-based timeline on the proper name Algebraic Number Theory, since editorial decisions to include or exclude events is purely a linguistic process. The resulting entries are used under license or with permission, used under "fair use" conditions, used in agreement with the original authors, or are in the public domain. ... Read more