L Functions For The Orthogonal Group

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L Functions For The Orthogonal Group

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Author : David Ginzburg
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

L Functions For The Orthogonal Group written by David Ginzburg 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 1997 with Mathematics categories.

In this book, the authors establish global Rankin Selberg integrals which determine the standard [italic capital]L function for the group [italic capitals]GL[subscript italic]r x [italic capital]Gʹ, where [italic capital]Gʹ is an isometry group of a nondegenerate symmetric form. The class of automorphic representations considered here is for any pair [capital Greek]Pi1 [otimes/dyadic/Kronecker/tensor product symbol] [capital Greek]Pi2 where [capital Greek]Pi1 is generic cuspidal for [italic capitals]GL[subscript italic]r([italic capital]A) and [capital Greek]Pi2 is cuspidal for [italic capital]Gʹ([italic capital]A). The construction of these [italic capital]L functions involves the use of certain new "models" of local representations; these models generalize the usual generic models. The authors also computer local unramified factors in a new way using geometric ideas.

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.

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.

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.

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.

Non Archimedean L Functions

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Author : Alexei A. Panchishkin
language : en
Publisher: Springer
Release Date : 2013-11-11

Non Archimedean L Functions written by Alexei A. Panchishkin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.

1) p n=1 The set of arguments s for which ((s) is defined can be extended to all s E C,s :f:. 1, and we may regard C as the group of all continuous quasicharacters C = Hom(R~, c>

Automorphic Forms Representations And L Functions

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Author : A. Borel
language : en
Publisher: American Mathematical Soc.
Release Date : 1979

Automorphic Forms Representations And L Functions written by A. Borel 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 1979 with Mathematics categories.

Contains sections on Reductive groups, representations, Automorphic forms and representations.

Degree 16 Standard L Function Of Gsp 2 Times Gsp 2

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Author : Dihua Jiang
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Degree 16 Standard L Function Of Gsp 2 Times Gsp 2 written by Dihua Jiang 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 1996 with Mathematics categories.

Automorphic L-functions, introduced by Robert Langlands in the 1960s, are natural extensions of such classical L-functions as the Riemann zeta function, Hecke L-functions, etc. They form an important part of the Langlands Program, which seeks to establish connections among number theory, representation theory, and geometry. This book offers, via the Rankin-Selberg method, a thorough and comprehensive examination of the degree 16 standard L-function of the product of two rank two symplectic similitude groups, which includes the study of the global integral of Rankin-Selberg type and local integrals, analytic properties of certain Eisenstein series of symplectic groups, and the relevant residue representations.

L Functions And Arithmetic

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Author : J. Coates
language : en
Publisher: Cambridge University Press
Release Date : 1991-02-22

L Functions And Arithmetic written by J. Coates 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 1991-02-22 with Mathematics categories.

Aimed at presenting nontechnical explanations, all the essays in this collection of papers from the 1989 LMS Durham Symposium on L-functions are the contributions of renowned algebraic number theory specialists.

The Riemann Hypothesis

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Author : Peter B. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2008

The Riemann Hypothesis written by Peter B. Borwein 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 2008 with Mathematics categories.

The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.