Elementary Theory of Eisenstein Series PDF Download

Author: Tomio Kubota
Publisher: Halsted Press
ISBN:
Category : Mathematics
Languages : en
Pages : 136

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Book Description

Author: Haruzo Hida
Publisher: Cambridge University Press
ISBN: 9780521435697
Category : Mathematics
Languages : en
Pages : 404

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Book Description
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.

Author: Goro Shimura
Publisher: Springer Science & Business Media
ISBN: 0387724745
Category : Mathematics
Languages : en
Pages : 151

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Book Description
A book on any mathematical subject beyond the textbook level is of little value unless it contains new ideas and new perspectives. It helps to include new results, provided that they give the reader new insights and are presented along with known old results in a clear exposition. It is with this philosophy that the author writes this volume. The two subjects, Dirichlet series and modular forms, are traditional subjects, but here they are treated in both orthodox and unorthodox ways. Regardless of the unorthodox treatment, the author has made the book accessible to those who are not familiar with such topics by including plenty of expository material.

Author: Colette Moeglin
Publisher: Cambridge University Press
ISBN: 9780521418935
Category : Mathematics
Languages : en
Pages : 382

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Book Description
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.

Author: Philipp Fleig
Publisher: Cambridge Studies in Advanced
ISBN: 1107189926
Category : Mathematics
Languages : en
Pages : 587

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Book Description
Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.

Author: Robert P. Langlands
Publisher: Springer
ISBN: 3540380701
Category : Mathematics
Languages : en
Pages : 344

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Book Description

Author: Goro Shimura
Publisher: Springer Science & Business Media
ISBN: 146142125X
Category : Mathematics
Languages : en
Pages : 183

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Book Description
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.

Author: B. Schoeneberg
Publisher: Springer Science & Business Media
ISBN: 3642656633
Category : Mathematics
Languages : en
Pages : 244

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Book Description
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.

Author:
Publisher: Academic Press
ISBN: 0080874150
Category : Mathematics
Languages : en
Pages : 401

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Book Description
The Theory of Eisenstein Systems

Author: Eberhard Freitag
Publisher: Springer Science & Business Media
ISBN: 3662026384
Category : Mathematics
Languages : en
Pages : 255

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Book Description
Important results on the Hilbert modular group and Hilbert modular forms are introduced and described in this book. In recent times, this branch of number theory has been given more and more attention and thus the need for a comprehensive presentation of these results, previously scattered in research journal papers, has become obvious. The main aim of this book is to give a description of the singular cohomology and its Hodge decomposition including explicit formulae. The author has succeeded in giving proofs which are both elementary and complete. The book contains an introduction to Hilbert modular forms, reduction theory, the trace formula and Shimizu's formulae, the work of Matsushima and Shimura, analytic continuation of Eisenstein series, the cohomology and its Hodge decomposition. Basic facts about algebraic numbers, integration, alternating differential forms and Hodge theory are included in convenient appendices so that the book can be used by students with a knowledge of complex analysis (one variable) and algebra.