Elementary Theory Of Eisenstein Series

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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.

Elementary Theory Of Eisenstein Series

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Author : Tomio Kubota
language : en
Publisher: Halsted Press
Release Date : 1973

Elementary Theory Of Eisenstein Series written by Tomio Kubota and has been published by Halsted Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematics categories.

Euler Products And Eisenstein Series

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Author : Gorō Shimura
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Euler Products And Eisenstein Series written by Gorō Shimura 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.

This volume has three chief objectives: 1) the determination of local Euler factors on classical groups in an explicit rational form; 2) Euler products and Eisenstein series on a unitary group of an arbitrary signature; and 3) a class number formula for a totally definite hermitian form. Though these are new results that have never before been published, Shimura starts with a quite general setting. He includes many topics of an expository nature so that the book can be viewed as an introduction to the theory of automorphic forms of several variables, Hecke theory in particular. Eventually, the exposition is specialized to unitary groups, but they are treated as a model case so that the reader can easily formulate the corresponding facts for other groups. There are various facts on algebraic groups and their localizations that are standard but were proved in some old papers or just called well-known. In this book, the reader will find the proofs of many of them, as well as systematic expositions of the topics. This is the first book in which the Hecke theory of a general (nonsplit) classical group is treated. The book is practically self-contained, except that familiarity with algebraic number theory is assumed.

Spectral Decomposition And Eisenstein Series

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Author : Colette Moeglin
language : en
Publisher: Cambridge University Press
Release Date : 1995-11-02

Spectral Decomposition And Eisenstein Series written by Colette Moeglin 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 1995-11-02 with Mathematics categories.

A self-contained introduction to automorphic forms, and Eisenstein series and pseudo-series, proving some of Langlands' work at the intersection of number theory and group theory.

Scattering Operator Eisenstein Series Inner Product Formula And Maass Selberg Relations For Kleinian Groups

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Author : Nikolaos Mandouvalos
language : en
Publisher: American Mathematical Soc.
Release Date : 1989

Scattering Operator Eisenstein Series Inner Product Formula And Maass Selberg Relations For Kleinian Groups written by Nikolaos Mandouvalos 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 1989 with Mathematics categories.

In this memoir we have introduced and studied the scattering operator and the Eisenstein series and we have formulated and proved the inner product formula and the "Maass-Selberg" relations for Kleinian groups.

On The Functional Equations Satisfied By Eisenstein Series

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Author : Robert P. Langlands
language : en
Publisher: Springer
Release Date : 2006-11-14

On The Functional Equations Satisfied By Eisenstein Series written by Robert P. Langlands and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Modular Forms Basics And Beyond

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Author : Goro Shimura
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-18

Modular Forms Basics And Beyond written by Goro Shimura 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 2011-11-18 with Mathematics categories.

This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically.

Elliptic Modular Functions

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Author : B. Schoeneberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Elliptic Modular Functions written by B. Schoeneberg 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 2012-12-06 with Mathematics categories.

This book is a fully detailed introduction to the theory of modular functions of a single variable. I hope that it will fill gaps which in view ofthe lively development ofthis theory have often been an obstacle to the students' progress. The study of the book requires an elementary knowledge of algebra, number theory and topology and a deeper knowledge of the theory of functions. An extensive discussion of the modular group SL(2, Z) is followed by the introduction to the theory of automorphic functions and auto morphic forms of integral dimensions belonging to SL(2,Z). The theory is developed first via the Riemann mapping theorem and then again with the help of Eisenstein series. An investigation of the subgroups of SL(2, Z) and the introduction of automorphic functions and forms belonging to these groups folIows. Special attention is given to the subgroups of finite index in SL (2, Z) and, among these, to the so-called congruence groups. The decisive role in this setting is assumed by the Riemann-Roch theorem. Since its proof may be found in the literature, only the pertinent basic concepts are outlined. For the extension of the theory, special fields of modular functions in particular the transformation fields of order n-are studied. Eisen stein series of higher level are introduced which, in case of the dimension - 2, allow the construction of integrals of the 3 rd kind. The properties of these integrals are discussed at length.

The Meromorphic Continuation And Functional Equations Of Cuspidal Eisenstein Series For Maximal Cuspidal Subgroups

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Author : Shek-Tung Wong
language : en
Publisher: American Mathematical Soc.
Release Date : 1990

The Meromorphic Continuation And Functional Equations Of Cuspidal Eisenstein Series For Maximal Cuspidal Subgroups written by Shek-Tung Wong 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 1990 with Mathematics categories.

We carry out, in the context of an algebraic group and an arithmetic subgroup, an idea of Selberg for continuing Eisenstein series. It makes use of the theory of integral operators. The meromorphic continuation and functional equation of an Eisenstein series constructed with a cusp form on the Levi component of a rank one cuspidal subgroup are established.

Elementary Theory Of Groups And Group Rings And Related Topics

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Author : Paul Baginski
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-02-10

Elementary Theory Of Groups And Group Rings And Related Topics written by Paul Baginski and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-10 with Mathematics categories.

This proceedings volume documents the contributions presented at the conference held at Fairfield University and at the Graduate Center, CUNY in 2018 celebrating the New York Group Theory Seminar, in memoriam Gilbert Baumslag, and to honor Benjamin Fine and Anthony Gaglione. It includes several expert contributions by leading figures in the group theory community and provides a valuable source of information on recent research developments.