Non Vanishing Of L Functions And Applications

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Non-vanishing of L-Functions and Applications

Author : M. Ram Murty
Publisher : Springer Science & Business Media
ISBN 13 : 3034802749
Total Pages : 206 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Non-vanishing of L-Functions and Applications by : M. Ram Murty

Download or read book Non-vanishing of L-Functions and Applications written by M. Ram Murty and published by Springer Science & Business Media. This book was released on 2012-01-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : M. Ram Murty
Publisher : Springer Science & Business Media
ISBN 13 : 3034802730
Total Pages : 205 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Non-vanishing of L-Functions and Applications by : M. Ram Murty

Download or read book Non-vanishing of L-Functions and Applications written by M. Ram Murty and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Ram M. Murty
Publisher :
ISBN 13 : 9783034889575
Total Pages : 212 pages
Book Rating : 4.8/5 (895 download)

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Book Synopsis Non-Vanishing of L-Functions and Applications by : Ram M. Murty

Download or read book Non-Vanishing of L-Functions and Applications written by Ram M. Murty and published by . This book was released on 2014-01-15 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-vanishing of L-functions and Applications

Author : Maruti Ram Murty
Publisher :
ISBN 13 :
Total Pages : 185 pages
Book Rating : 4.:/5 (772 download)

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Book Synopsis Non-vanishing of L-functions and Applications by : Maruti Ram Murty

Download or read book Non-vanishing of L-functions and Applications written by Maruti Ram Murty and published by . This book was released on 1995 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advanced Analytic Number Theory: L-Functions

Author : Carlos J. Moreno
Publisher : American Mathematical Soc.
ISBN 13 : 0821842668
Total Pages : 313 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Advanced Analytic Number Theory: L-Functions by : Carlos J. Moreno

Download or read book Advanced Analytic Number Theory: L-Functions written by Carlos J. Moreno and published by American Mathematical Soc.. This book was released on 2005 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : James W. Cogdell
Publisher : Walter de Gruyter
ISBN 13 : 3110892707
Total Pages : 441 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Automorphic Representations, L-Functions and Applications: Progress and Prospects by : James W. Cogdell

Download or read book Automorphic Representations, L-Functions and Applications: Progress and Prospects written by James W. Cogdell and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Cristian Popescu
Publisher : American Mathematical Soc.
ISBN 13 : 0821886983
Total Pages : 517 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Arithmetic of L-functions by : Cristian Popescu

Download or read book Arithmetic of L-functions written by Cristian Popescu and published by American Mathematical Soc.. This book was released on with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory

Author : Solomon Friedberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821839632
Total Pages : 320 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory by : Solomon Friedberg

Download or read book Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory written by Solomon Friedberg and published by American Mathematical Soc.. This book was released on 2006 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Daniel Bump
Publisher : Springer
ISBN 13 : 0817683348
Total Pages : 367 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Multiple Dirichlet Series, L-functions and Automorphic Forms by : Daniel Bump

Download or read book Multiple Dirichlet Series, L-functions and Automorphic Forms written by Daniel Bump and published by Springer. This book was released on 2012-07-09 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Jörn Steuding
Publisher : Springer
ISBN 13 : 3540448225
Total Pages : 320 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Value-Distribution of L-Functions by : Jörn Steuding

Download or read book Value-Distribution of L-Functions written by Jörn Steuding and published by Springer. This book was released on 2007-05-26 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algorithmic Number Theory

Author : Alf J. van der Poorten
Publisher : Springer Science & Business Media
ISBN 13 : 3540794557
Total Pages : 463 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Algorithmic Number Theory by : Alf J. van der Poorten

Download or read book Algorithmic Number Theory written by Alf J. van der Poorten and published by Springer Science & Business Media. This book was released on 2008-04-25 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008. The 28 revised full papers presented together with 2 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on elliptic curves cryptology and generalizations, arithmetic of elliptic curves, integer factorization, K3 surfaces, number fields, point counting, arithmetic of function fields, modular forms, cryptography, and number theory.

Number Theory and Applications

Author : S.D. Adhikari
Publisher : Springer
ISBN 13 : 9386279460
Total Pages : 285 pages
Book Rating : 4.3/5 (862 download)

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Book Synopsis Number Theory and Applications by : S.D. Adhikari

Download or read book Number Theory and Applications written by S.D. Adhikari and published by Springer. This book was released on 2009-06-15 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.

Automorphic Forms and $L$-functions I

Author : David Ginzburg
Publisher : American Mathematical Soc.
ISBN 13 : 0821847066
Total Pages : 315 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Automorphic Forms and $L$-functions I by : David Ginzburg

Download or read book Automorphic Forms and $L$-functions I written by David Ginzburg and published by American Mathematical Soc.. This book was released on 2009 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes articles that represent global aspects of automorphic forms. This book covers topics such as: the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions.

Ranks of Elliptic Curves and Random Matrix Theory

Author : J. B. Conrey
Publisher : Cambridge University Press
ISBN 13 : 0521699649
Total Pages : 5 pages
Book Rating : 4.5/5 (216 download)

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Book Synopsis Ranks of Elliptic Curves and Random Matrix Theory by : J. B. Conrey

Download or read book Ranks of Elliptic Curves and Random Matrix Theory written by J. B. Conrey and published by Cambridge University Press. This book was released on 2007-02-08 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume introduces elliptic curves and the fundamentals of modeling by a family of random matrices.

Non-vanishing of L-functions and Their Derivatives

Author : Vijaya Kumar Murty
Publisher :
ISBN 13 :
Total Pages : 50 pages
Book Rating : 4.:/5 (225 download)

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Book Synopsis Non-vanishing of L-functions and Their Derivatives by : Vijaya Kumar Murty

Download or read book Non-vanishing of L-functions and Their Derivatives written by Vijaya Kumar Murty and published by . This book was released on 1989 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Equivalents of the Riemann Hypothesis: Volume 2, Analytic Equivalents

Author : Kevin Broughan
Publisher : Cambridge University Press
ISBN 13 : 1108187021
Total Pages : 513 pages
Book Rating : 4.1/5 (81 download)

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Book Synopsis Equivalents of the Riemann Hypothesis: Volume 2, Analytic Equivalents by : Kevin Broughan

Download or read book Equivalents of the Riemann Hypothesis: Volume 2, Analytic Equivalents written by Kevin Broughan and published by Cambridge University Press. This book was released on 2017-11-02 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.

Non-Vanishing of the Derivative of L-Functions at the Central Point

Author : Matthew Dolan Jobrack
Publisher :
ISBN 13 :
Total Pages : 70 pages
Book Rating : 4.6/5 (781 download)

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Book Synopsis Non-Vanishing of the Derivative of L-Functions at the Central Point by : Matthew Dolan Jobrack

Download or read book Non-Vanishing of the Derivative of L-Functions at the Central Point written by Matthew Dolan Jobrack and published by . This book was released on 2020 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: L-functions are complex analytic functions attached to various objects of interest in number theory. The distribution of the zeros of an L-function is often of particular interest, due to their relationship with the objects associated to L-functions as well as connections to deep questions about the theory of L-functions in general. Here we consider derivatives of L-functions associated to classical modular forms of large weight.In particular, we derive a lower bound for the proportion of such derivatives which are non-vanishing at the point s=1/2, which is the central point of a functional equation satisfied by the L-functions. This is accomplished by computing the first and second moments of the L-function derivatives. We then attach objects known as mollifiers to these moments, and attempt to choose coefficients within the mollifiers to optimize the ratio between the square of the first mollified moment and the second mollified moment. By Cauchy's inequality, this ratio gives a lower bound for the proportion of L-function derivatives which are non-vanishing. By our choice of mollifier, we can deduce that the proportion of L-function derivatives associated to modular forms of large weight which do not vanish at s=1/2 is at least .398.