[PDF] Starks Conjectures Recent Work And New Directions eBook

Author : David Burns
Publisher : American Mathematical Soc.
Page : 234 pages
File Size : 28,80 MB
Release : 2004
Category : Education
ISBN : 0821834800

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Stark's conjectures on the behavior of USDLUSD-functions were formulated in the 1970s. Since then, these conjectures and their generalizations have been actively investigated. This has led to significant progress in algebraic number theory. The current volume, based on the conference held at Johns Hopkins University (Baltimore, MD), represents the state-of-the-art research in this area. The first four survey papers provide an introduction to a majority of the recent work related to themes currently under exploration in the area, such as non-abelian and USDpUSD-adic aspects of the conjectures, abelian refinements, etc. Among others, some important contributors to the volume include Harold M. Stark, John Tate, and interested in number theory.

Author : David Burns
Publisher : American Mathematical Soc.
Page : 238 pages
File Size : 39,96 MB
Release : 2004-09-16
Category : Stark's conjectures
ISBN : 9780821856932

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Stark's conjectures on the behavior of $L$-functions were formulated in the 1970s. Since then, these conjectures and their generalizations have been actively investigated. This has led to significant progress in algebraic number theory. The current volume, based on the conference held at Johns Hopkins University (Baltimore, MD), represents the state-of-the-art research in this area. The first four survey papers provide an introduction to a majority of the recent work related to Stark's conjectures. The remaining six contributions touch on some major themes currently under exploration in the area, such as non-abelian and $p$-adic aspects of the conjectures, abelian refinements, etc. Among others, some important contributors to the volume include Harold M. Stark, John Tate, and Barry Mazur. The book is suitable for graduate students and researchers interested in number theory.

Author : John Coates
Publisher : Cambridge University Press
Page : 317 pages
File Size : 41,95 MB
Release : 2015-03-13
Category : Mathematics
ISBN : 1107492963

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A graduate-level account of an important recent result concerning the Riemann zeta function.

Author : Chantal David
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 30,92 MB
Release : 2013-12-10
Category : Mathematics
ISBN : 1470410222

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The second Women in Numbers workshop (WIN2) was held November 6-11, 2011, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. During the workshop, group leaders presented open problems in various areas of number theory, and working groups tackled those problems in collaborations begun at the workshop and continuing long after. This volume collects articles written by participants of WIN2. Survey papers written by project leaders are designed to introduce areas of active research in number theory to advanced graduate students and recent PhDs. Original research articles by the project groups detail their work on the open problems tackled during and after WIN2. Other articles in this volume contain new research on related topics by women number theorists. The articles collected here encompass a wide range of topics in number theory including Galois representations, the Tamagawa number conjecture, arithmetic intersection formulas, Mahler measures, Newton polygons, the Dwork family, elliptic curves, cryptography, and supercongruences. WIN2 and this Proceedings volume are part of the Women in Numbers network, aimed at increasing the visibility of women researchers' contributions to number theory and at increasing the participation of women mathematicians in number theory and related fields. This book is co-published with the Centre de Recherches Mathématiques.

Author : Florian Hess
Publisher : Springer
Page : 609 pages
File Size : 35,77 MB
Release : 2006-10-05
Category : Mathematics
ISBN : 354036076X

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This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, July 2006. The book presents 37 revised full papers together with 4 invited papers selected for inclusion. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves over finite fields and applications, and discrete logarithms.

Author : Barry Mazur
Publisher : American Mathematical Soc.
Page : 786 pages
File Size : 28,73 MB
Release : 2016-12-13
Category : Mathematics
ISBN : 082189093X

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In these volumes, a reader will find all of John Tate's published mathematical papers—spanning more than six decades—enriched by new comments made by the author. Included also is a selection of his letters. His letters give us a close view of how he works and of his ideas in process of formation.

Author : François Brunault
Publisher : Cambridge University Press
Page : 185 pages
File Size : 41,83 MB
Release : 2020-05-14
Category : Mathematics
ISBN : 1108889190

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The Mahler measure is a fascinating notion and an exciting topic in contemporary mathematics, interconnecting with subjects as diverse as number theory, analysis, arithmetic geometry, special functions and random walks. This friendly and concise introduction to the Mahler measure is a valuable resource for both graduate courses and self-study. It provides the reader with the necessary background material, before presenting the recent achievements and the remaining challenges in the field. The first part introduces the univariate Mahler measure and addresses Lehmer's question, and then discusses techniques of reducing multivariate measures to hypergeometric functions. The second part touches on the novelties of the subject, especially the relation with elliptic curves, modular forms and special values of L-functions. Finally, the Appendix presents the modern definition of motivic cohomology and regulator maps, as well as Deligne–Beilinson cohomology. The text includes many exercises to test comprehension and challenge readers of all abilities.

Author : John Coates
Publisher : Cambridge University Press
Page : 321 pages
File Size : 21,24 MB
Release : 2011-12-15
Category : Mathematics
ISBN : 1139505653

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This book describes the interaction between several key aspects of Galois theory based on Iwasawa theory, fundamental groups and automorphic forms. These ideas encompass a large portion of mainstream number theory and ramifications that are of interest to graduate students and researchers in number theory, algebraic geometry, topology and physics.

Author : Sirakov Boyan
Publisher : World Scientific
Page : 5396 pages
File Size : 23,70 MB
Release : 2019-02-27
Category : Mathematics
ISBN : 9813272899

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The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.