Non Vanishing Of L Functions And Applications
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Non Vanishing Of L Functions And Applications
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Author : Ram M. Murty
language : en
Publisher: Birkhäuser
Release Date : 2013-11-09
Non Vanishing Of L Functions And Applications written by Ram M. Murty and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Mathematics categories.
This monograph brings together a collection of results on the non-vanishing of L functions. The presentation, though based largely on the original papers, is suitable for independent study. A number of exercises have also been provided to aid in this endeavour. The exercises are of varying difficulty and those which require more effort have been marked with an asterisk. The authors would like to thank the Institut d'Estudis Catalans for their encouragement of this work through the Ferran Sunyer i Balaguer Prize. We would also like to thank the Institute for Advanced Study, Princeton for the excellent conditions which made this work possible, as well as NSERC, NSF and FCAR for funding. Princeton M. Ram Murty August, 1996 V. Kumar Murty Introduction Since the time of Dirichlet and Riemann, the analytic properties of L-functions have been used to establish theorems of a purely arithmetic nature. The distri bution of prime numbers in arithmetic progressions is intimately connected with non-vanishing properties of various L-functions. With the subsequent advent of the Tauberian theory as developed by Wiener and Ikehara, these arithmetical the orems have been shown to be equivalent to the non-vanishing of these L-functions on the line Re(s) = 1. In the 1950's, a new theme was introduced by Birch and Swinnerton-Dyer.
Non Vanishing Of L Functions And Applications
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Author : M. Ram Murty
language : en
Publisher: Birkhäuser
Release Date : 2012-01-26
Non Vanishing Of L Functions And Applications written by M. Ram Murty and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-26 with Mathematics categories.
This volume develops methods for proving the non-vanishing of certain L-functions at points in the critical strip. It begins at a very basic level and continues to develop, providing readers with a theoretical foundation that allows them to understand the latest discoveries in the field.
Non Vanishing Of L Functions And Applications
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Author : Maruti Ram Murty
language : en
Publisher:
Release Date : 1995
Non Vanishing Of L Functions And Applications written by Maruti Ram Murty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with L-functions categories.
Non Vanishing Of L Functions And Applications
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Author : M. Ram Murty
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-05
Non Vanishing Of L Functions And Applications written by M. Ram Murty and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-05 with Mathematics categories.
This volume develops methods for proving the non-vanishing of certain L-functions at points in the critical strip. It begins at a very basic level and continues to develop, providing readers with a theoretical foundation that allows them to understand the latest discoveries in the field.
Advanced Analytic Number Theory L Functions
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Author : Carlos J. Moreno
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Advanced Analytic Number Theory L Functions written by Carlos J. Moreno and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Algebraic number theory categories.
Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.
Automorphic Representations L Functions And Applications Progress And Prospects
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Author : James W. Cogdell
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24
Automorphic Representations L Functions And Applications Progress And Prospects written by James W. Cogdell and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.
This volume is the proceedings of the conference on Automorphic Representations, L-functions and Applications: Progress and Prospects, held at the Department of Mathematics of The Ohio State University, March 27–30, 2003, in honor of the 60th birthday of Steve Rallis. The theory of automorphic representations, automorphic L-functions and their applications to arithmetic continues to be an area of vigorous and fruitful research. The contributed papers in this volume represent many of the most recent developments and directions, including Rankin–Selberg L-functions (Bump, Ginzburg–Jiang–Rallis, Lapid–Rallis) the relative trace formula (Jacquet, Mao–Rallis) automorphic representations (Gan–Gurevich, Ginzburg–Rallis–Soudry) representation theory of p-adic groups (Baruch, Kudla–Rallis, Mœglin, Cogdell–Piatetski-Shapiro–Shahidi) p-adic methods (Harris–Li–Skinner, Vigneras), and arithmetic applications (Chinta–Friedberg–Hoffstein). The survey articles by Bump, on the Rankin–Selberg method, and by Jacquet, on the relative trace formula, should be particularly useful as an introduction to the key ideas about these important topics. This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field.
Arithmetic Of L Functions
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Author : Cristian Popescu
language : en
Publisher: American Mathematical Soc.
Release Date :
Arithmetic Of L Functions written by Cristian Popescu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Multiple Dirichlet Series Automorphic Forms And Analytic Number Theory
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Author : Bretton Woods Workshop on Multiple Dirichlet Series
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Multiple Dirichlet Series Automorphic Forms And Analytic Number Theory written by Bretton Woods Workshop on Multiple Dirichlet Series and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Dirichlet series categories.
Multiple Dirichlet series are Dirichlet series in several complex variables. A multiple Dirichlet series is said to be perfect if it satisfies a finite group of functional equations and has meromorphic continuation everywhere. The earliest examples came from Mellin transforms of metaplectic Eisenstein series and have been intensively studied over the last twenty years. More recently, many other examples have been discovered and it appears that all the classical theorems on moments of $L$-functions as well as the conjectures (such as those predicted by random matrix theory) can now be obtained via the theory of multiple Dirichlet series. Furthermore, new results, not obtainable by other methods, are just coming to light. This volume offers an account of some of the major research to date and the opportunities for the future. It includes an exposition of the main results in the theory of multiple Dirichlet series, and papers on moments of zeta- and $L$-functions, on new examples of multiple Dirichlet
Multiple Dirichlet Series L Functions And Automorphic Forms
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Author : Daniel Bump
language : en
Publisher: Springer
Release Date : 2012-07-09
Multiple Dirichlet Series L Functions And Automorphic Forms written by Daniel Bump and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-09 with Mathematics categories.
Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representation theory, mathematical physics, and special functions. Contributors: J. Beineke, B. Brubaker, D. Bump, G. Chinta, G. Cornelissen, C.A. Diaconu, S. Frechette, S. Friedberg, P. Garrett, D. Goldfeld, P.E. Gunnells, B. Heim, J. Hundley, D. Ivanov, Y. Komori, A.V. Kontorovich, O. Lorscheid, K. Matsumoto, P.J. McNamara, S.J. Patterson, M. Suzuki, H. Tsumura.
Value Distribution Of L Functions
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Author : Jörn Steuding
language : en
Publisher: Springer
Release Date : 2007-05-26
Value Distribution Of L Functions written by Jörn Steuding and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-26 with Mathematics categories.
These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.