On Certain L Functions
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On Certain L Functions
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Author : James Arthur
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
On Certain L Functions written by James Arthur 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 2011 with Mathematics categories.
Illuminate various areas of the study of geometric, analytic, and number theoretic aspects of automorphic forms and their $L$-functions, and both local and global theory are addressed. Topics discussed in the articles include Langlands functoriality, the Rankin-Selberg method, the Langlands-Shahidi method, motivic Galois groups, Shimura varieties, orbital integrals, representations of $p$-adic groups, Plancherel formula and its consequences, and the Gross-Prasad conjecture.
Explicit Constructions Of Automorphic L Functions
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Author : Stephen Gelbart
language : en
Publisher: Springer
Release Date : 2006-11-15
Explicit Constructions Of Automorphic L Functions written by Stephen Gelbart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The goal of this research monograph is to derive the analytic continuation and functional equation of the L-functions attached by R.P. Langlands to automorphic representations of reductive algebraic groups. The first part of the book (by Piatetski-Shapiro and Rallis) deals with L-functions for the simple classical groups; the second part (by Gelbart and Piatetski-Shapiro) deals with non-simple groups of the form G GL(n), with G a quasi-split reductive group of split rank n. The method of proof is to construct certain explicit zeta-integrals of Rankin-Selberg type which interpolate the relevant Langlands L-functions and can be analyzed via the theory of Eisenstein series and intertwining operators. This is the first time such an approach has been applied to such general classes of groups. The flavor of the local theory is decidedly representation theoretic, and the work should be of interest to researchers in group representation theory as well as number theory.
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.
Elementary Theory Of L Functions And Eisenstein Series
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Author : Haruzo Hida
language : en
Publisher: Cambridge University Press
Release Date : 1993-02-11
Elementary Theory Of L Functions And Eisenstein Series written by Haruzo Hida and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-02-11 with Mathematics categories.
The theory of p-adic and classic modular forms, and the study of arithmetic and p-adic L-functions has proved to be a fruitful area of mathematics over the last decade. Professor Hida has given courses on these topics in the USA, Japan, and in France, and in this book provides the reader with an elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise, and the subject is approached using only basic tools from complex analysis and cohomology theory. Graduate students wishing to know more about L-functions will find that this book offers a unique introduction to this fascinating branch of mathematics.
Automorphic Forms And L Functions For The Group Gl N R
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Author : Dorian Goldfeld
language : en
Publisher: Cambridge University Press
Release Date : 2015-11-26
Automorphic Forms And L Functions For The Group Gl N R written by Dorian Goldfeld and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-26 with Mathematics categories.
L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.
Analytic Properties Of Automorphic L Functions
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Author : Stephen Gelbart
language : en
Publisher: Academic Press
Release Date : 2014-07-14
Analytic Properties Of Automorphic L Functions written by Stephen Gelbart and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
Analytic Properties of Automorphic L-Functions is a three-chapter text that covers considerable research works on the automorphic L-functions attached by Langlands to reductive algebraic groups. Chapter I focuses on the analysis of Jacquet-Langlands methods and the Einstein series and Langlands’ so-called “Euler products . This chapter explains how local and global zeta-integrals are used to prove the analytic continuation and functional equations of the automorphic L-functions attached to GL(2). Chapter II deals with the developments and refinements of the zeta-inetgrals for GL(n). Chapter III describes the results for the L-functions L (s, ?, r), which are considered in the constant terms of Einstein series for some quasisplit reductive group. This book will be of value to undergraduate and graduate mathematics students.
L Functions And The Oscillator Representation
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Author : Stephen Rallis
language : en
Publisher: Springer
Release Date : 2006-11-15
L Functions And The Oscillator Representation written by Stephen Rallis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
These notes are concerned with showing the relation between L-functions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q). The problem of measuring the nonvanishing of a *F2 correspondence by computing the Petersson inner product of a *F2 lift from *F1 to O(Q) is considered. This product can be expressed as the special value of an L-function (associated to the standard representation of the L-group of *F1) times a finite number of local Euler factors (measuring whether a given local representation occurs in a given oscillator representation). The key ideas used in proving this are (i) new Rankin integral representations of standard L-functions, (ii) see-saw dual reductive pairs and (iii) Siegel-Weil formula. The book addresses readers who specialize in the theory of automorphic forms and L-functions and the representation theory of Lie groups. N
Automorphic Forms And L Functions For The Group Gl N R
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Author : Dorian Goldfeld
language : en
Publisher: Cambridge University Press
Release Date : 2006-08-03
Automorphic Forms And L Functions For The Group Gl N R written by Dorian Goldfeld and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-03 with Mathematics categories.
L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.
Non Vanishing Of L Functions And Applications
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Author : Maruti Ram Murty
language : en
Publisher: Springer Science & Business Media
Release Date : 1997
Non Vanishing Of L Functions And Applications written by Maruti 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 1997 with Mathematics categories.
Discussion of results on the nonvanishing of L-functions is largely based on the various mathematicians' original papers. The authors place special emphasis on L-functions of Dirichlet and Artin, and those that are attached to modular forms. They address theorems on nonvanishing that have immediate applications to general questions concerning equidistribution. They do not consider the Galois theoretic and the automorphic method. Annotation copyrighted by Book News, Inc., Portland, OR
L Functions And Automorphic Forms
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Author : Jan Hendrik Bruinier
language : en
Publisher: Springer
Release Date : 2018-02-22
L Functions And Automorphic Forms written by Jan Hendrik Bruinier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-22 with Mathematics categories.
This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways. The 19 papers cover a wide range of topics within the scope of the conference, including automorphic L-functions and their special values, p-adic modular forms, Eisenstein series, Borcherds products, automorphic periods, and many more.