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Author: Heng Huat Chan
Publisher: de Gruyter
ISBN: 9783110540710
Category : Elliptic functions
Languages : en
Pages : 0
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Book Description
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 [pi] PDF](https://books.google.com/books/content/images/frontcover/DXF9zQEACAAJ?fife=w80-h100)
Author: Heng Huat Chan
Publisher: de Gruyter
ISBN: 9783110540710
Category : Elliptic functions
Languages : en
Pages : 0
Get Book Here
Book Description
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.
Author: Heng Huat Chan
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110541912
Category : Mathematics
Languages : en
Pages : 138
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Book Description
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.
Author: Richard Bellman
Publisher: Courier Corporation
ISBN: 0486492958
Category : Mathematics
Languages : en
Pages : 100
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Book Description
Originally published: New York: Rinehart and Winston, 1961.
Author: Hantaro Nagaoka
Publisher:
ISBN:
Category : Elliptic functions
Languages : en
Pages : 78
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Book Description
Author: Komaravolu Chandrasekharan
Publisher: Springer Science & Business Media
ISBN: 3642522440
Category : Mathematics
Languages : en
Pages : 199
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Book Description
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.
Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 1461247527
Category : Mathematics
Languages : en
Pages : 319
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Book Description
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.
Author: Shaun Cooper
Publisher: Springer
ISBN: 3319561723
Category : Mathematics
Languages : en
Pages : 696
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Book Description
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.
Author: Arthur B. Coble
Publisher: American Mathematical Soc.
ISBN: 0821846027
Category : Mathematics
Languages : en
Pages : 292
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Book Description
This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and genus three (Chapter IV). The case of genus four is discussed in the last chapter. The exposition is concise with a rich variety of details and references.
Author: Eric Temple Bell
Publisher:
ISBN:
Category : Elliptic functions
Languages : en
Pages : 338
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Book Description
Author: A. I. Markushevich
Publisher: American Mathematical Soc.
ISBN: 082183780X
Category : Analytic functions
Languages : en
Pages : 1178
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Book Description
