Theta Functions, Elliptic Functions and [pi]

Theta Functions, Elliptic Functions and [pi] PDF

Author: Heng Huat Chan

Publisher: de Gruyter

Published: 2020

Total Pages: 0

ISBN-13: 9783110540710

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This book presents several results on elliptic functions and Pi, using Jacobi's triple product identity as a tool to show suprising connections between different topics within number theory such as theta functions, Eisenstein series, the Dedekind delta function, and Ramanujan's work on Pi. The included exercises make it ideal for both classroom use and self-study.

Theta functions, elliptic functions and π

Theta functions, elliptic functions and π PDF

Author: Heng Huat Chan

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-07-06

Total Pages: 138

ISBN-13: 3110541912

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This book presents several results on elliptic functions and Pi, using Jacobi’s triple product identity as a tool to show suprising connections between different topics within number theory such as theta functions, Eisenstein series, the Dedekind delta function, and Ramanujan’s work on Pi. The included exercises make it ideal for both classroom use and self-study.

Elliptic Functions

Elliptic Functions PDF

Author: Komaravolu Chandrasekharan

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 199

ISBN-13: 3642522440

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This book has grown out of a course of lectures on elliptic functions, given in German, at the Swiss Federal Institute of Technology, Zurich, during the summer semester of 1982. Its aim is to give some idea of the theory of elliptic functions, and of its close connexion with theta-functions and modular functions, and to show how it provides an analytic approach to the solution of some classical problems in the theory of numbers. It comprises eleven chapters. The first seven are function-theoretic, and the next four concern arithmetical applications. There are Notes at the end of every chapter, which contain references to the literature, comments on the text, and on the ramifications, old and new, of the problems dealt with, some of them extending into cognate fields. The treatment is self-contained, and makes no special demand on the reader's knowledge beyond the elements of complex analysis in one variable, and of group theory.

Elliptic Functions

Elliptic Functions PDF

Author: Serge Lang

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 319

ISBN-13: 1461247527

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Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century. The book is divided into four parts. In the first, Lang presents the general analytic theory starting from scratch. Most of this can be read by a student with a basic knowledge of complex analysis. The next part treats complex multiplication, including a discussion of Deuring's theory of l-adic and p-adic representations, and elliptic curves with singular invariants. Part three covers curves with non-integral invariants, and applies the Tate parametrization to give Serre's results on division points. The last part covers theta functions and the Kronecker Limit Formula. Also included is an appendix by Tate on algebraic formulas in arbitrary charactistic.

Ramanujan's Theta Functions

Ramanujan's Theta Functions PDF

Author: Shaun Cooper

Publisher: Springer

Published: 2017-06-12

Total Pages: 696

ISBN-13: 3319561723

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Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research. Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter.

Elliptic Functions and Elliptic Integrals

Elliptic Functions and Elliptic Integrals PDF

Author: Viktor Vasil_evich Prasolov

Publisher: American Mathematical Soc.

Published: 1997-09-16

Total Pages: 202

ISBN-13: 9780821897805

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This book is devoted to the geometry and arithmetic of elliptic curves and to elliptic functions with applications to algebra and number theory. It includes modern interpretations of some famous classical algebraic theorems such as Abel's theorem on the lemniscate and Hermite's solution of the fifth degree equation by means of theta functions. Suitable as a text, the book is self-contained and assumes as prerequisites only the standard one-year courses of algebra and analysis.

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