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Modular Functions Of One Variable

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Modular Functions Of One Variable I

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Author : Kuyk
language : en
Publisher: Springer Science & Business Media
Release Date : 1973

Modular Functions Of One Variable I written by Kuyk 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 1973 with Mathematics categories.

An international Summer School on: "Modular functions of one variable and arithmetical applications" took place at RUCA, Antwerp University, from July 17 to - gust 3, 1972. This book is the first volume (in a series of four) of the Proceedings of the Summer School. It includes the basic course given by A. Ogg, and several other papers with a strong analyt~c flavour. Volume 2 contains the courses of R. P. Langlands (l-adic rep resentations) and P. Deligne (modular schemes - representations of GL ) and papers on related topics. 2 Volume 3 is devoted to p-adic properties of modular forms and applications to l-adic representations and zeta functions. Volume 4 collects various material on elliptic curves, includ ing numerical tables. The School was a NATO Advanced Study Institute, and the orga nizers want to thank NATO for its major subvention. Further support, in various forms, was received from IBM Belgium, the Coca-Cola Co. of Belgium, Rank Xerox Belgium, the Fort Food Co. of Belgium, and NSF Washington, D.C•• We extend our warm est thanks to all of them, as well as to RUCA and the local staff (not forgetting hostesses and secretaries!) who did such an excellent job.

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.

Modular Functions Of One Variable Iii

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Author : Willem Kuyk
language : en
Publisher: Springer
Release Date : 2009-02-27

Modular Functions Of One Variable Iii written by Willem Kuyk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-27 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.

Modular Functions Of One Variable Ii

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Author : P. Deligne
language : en
Publisher:
Release Date : 2014-01-15

Modular Functions Of One Variable Ii written by P. Deligne and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Modular Functions Of One Variable I

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Author : Kuyk
language : en
Publisher:
Release Date : 2014-01-15

Modular Functions Of One Variable I written by Kuyk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Introduction To Siegel Modular Forms And Dirichlet Series

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Author : Anatoli Andrianov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-22

Introduction To Siegel Modular Forms And Dirichlet Series written by Anatoli Andrianov 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 2008-12-22 with Mathematics categories.

Several years ago I was invited to an American university to give one-term graduate course on Siegel modular forms, Hecke operators, and related zeta functions. The idea to present in a concise but basically complete and self-contained form an int- duction to an important and developing area based partly on my own work attracted me. I accepted the invitation and started to prepare the course. Unfortunately, the visit was not realized. But the idea of such a course continued to be alive till after a number of years this book was ?nally completed. I hope that this short book will serve to attract young researchers to this beautiful ?eld, and that it will simplify and make more pleasant the initial steps. No special knowledge is presupposed for reading this book beyond standard courses in algebra and calculus (one and several variables), although some skill in working with mathematical texts would be helpful. The reader will judge whether the result was worth the effort. Dedications. The ideas of Goro Shimura exerted a deep in?uence on the number theory of the second half of the twentieth century in general and on the author’s formation in particular. When Andre ` Weil was signing a copy of his “Basic Number Theory” to my son, he wrote in Russian, ”To Fedor Anatolievich hoping that he will become a number theoretist”. Fedor has chosen computer science. Now I pass on the idea to Fedor’s daughter, Alexandra Fedorovna.

Modular Functions Of One Variable Iii

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Author : Willem Kuyk
language : en
Publisher: Springer
Release Date : 1986-02-01

Modular Functions Of One Variable I

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Author : Kuyk
language : en
Publisher: Springer
Release Date : 1986-02-01

Modular Functions Of One Variable I written by Kuyk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-02-01 with Mathematics categories.

The 1 2 3 Of Modular Forms

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Author : Jan Hendrik Bruinier
language : en
Publisher: Springer
Release Date : 2009-09-02

The 1 2 3 Of Modular 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 2009-09-02 with Mathematics categories.

This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.

Modular Functions Of One Variable

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