A Brief Introduction to Theta Functions
Author: Richard Bellman
Publisher: Courier Corporation
Published: 2013-01-01
Total Pages: 100
ISBN-13: 0486492958
DOWNLOAD EBOOK →Originally published: New York: Rinehart and Winston, 1961.
Lanterna Rally
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A Brief Introduction to Theta Functions
Theta Functions
Author: Maruti Ram Murty
Publisher: American Mathematical Soc.
Published: 1993-01-01
Total Pages: 188
ISBN-13: 9780821870112
DOWNLOAD EBOOK →This book contains lectures on theta functions written by experts well known for excellence in exposition. The lectures represent the content of four courses given at the Centre de Recherches Mathematiques in Montreal during the academic year 1991-1992, which was devoted to the study of automorphic forms. Aimed at graduate students, the book synthesizes the classical and modern points of view in theta functions, concentrating on connections to number theory and representation theory. An excellent introduction to this important subject of current research, this book is suitable as a text in advanced graduate courses.
Ramanujan's Theta Functions
Author: Shaun Cooper
Publisher: Springer
Published: 2017-06-12
Total Pages: 696
ISBN-13: 3319561723
DOWNLOAD EBOOK →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.
Tata Lectures on Theta I
Author: David Mumford
Publisher: Springer Science & Business Media
Published: 2007-06-25
Total Pages: 248
ISBN-13: 0817645772
DOWNLOAD EBOOK →This volume is the first of three in a series surveying the theory of theta functions. Based on lectures given by the author at the Tata Institute of Fundamental Research in Bombay, these volumes constitute a systematic exposition of theta functions, beginning with their historical roots as analytic functions in one variable (Volume I), touching on some of the beautiful ways they can be used to describe moduli spaces (Volume II), and culminating in a methodical comparison of theta functions in analysis, algebraic geometry, and representation theory (Volume III).
Theta Functions
Author: Jun-ichi Igusa
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 234
ISBN-13: 3642653154
DOWNLOAD EBOOK →The theory of theta functions has a long history; for this, we refer A. Krazer and W. Wirtinger the reader to an encyclopedia article by ("Sources" [9]). We shall restrict ourselves to postwar, i. e., after 1945, periods. Around 1948/49, F. Conforto, c. L. Siegel, A. Well reconsidered the main existence theorems of theta functions and found natural proofs for them. These are contained in Conforto: Abelsche Funktionen und algebraische Geometrie, Springer (1956); Siegel: Analytic functions of several complex variables, Lect. Notes, I.A.S. (1948/49); Well: Theoremes fondamentaux de la theorie des fonctions theta, Sem. Bourbaki, No. 16 (1949). The complete account of Weil's method appeared in his book of 1958 [20]. The next important achievement was the theory of compacti fication of the quotient variety of Siegel's upper-half space by a modular group. There are many ways to compactify the quotient variety; we are talking about what might be called a standard compactification. Such a compactification was obtained first as a Hausdorff space by I. Satake in "On the compactification of the Siegel space", J. Ind. Math. Soc. 20, 259-281 (1956), and as a normal projective variety by W.L. Baily in 1958 [1]. In 1957/58, H. Cartan took up this theory in his seminar [3]; it was shown that the graded ring of modular forms relative to the given modular group is a normal integral domain which is finitely generated over C
Conformal Blocks, Generalized Theta Functions and the Verlinde Formula
Author: Shrawan Kumar
Publisher: Cambridge University Press
Published: 2021-11-25
Total Pages: 539
ISBN-13: 1316518167
DOWNLOAD EBOOK →This book gives a complete proof of the Verlinde formula and of its connection to generalized theta functions.
A Brief Introduction to Theta Functions
Author: Richard Bellman
Publisher: Courier Corporation
Published: 2013-11-05
Total Pages: 96
ISBN-13: 0486782832
DOWNLOAD EBOOK →Brief but intriguing monograph on the theory of elliptic functions, written by a prominent mathematician. Spotlights high points of the fundamental regions and illustrates powerful, versatile analytic methods. 1961 edition.
Theta Functions on Riemann Surfaces
Author: J. D. Fay
Publisher: Springer
Published: 2006-11-15
Total Pages: 142
ISBN-13: 3540378154
DOWNLOAD EBOOK →These notes present new as well as classical results from the theory of theta functions on Riemann surfaces, a subject of renewed interest in recent years. Topics discussed here include: the relations between theta functions and Abelian differentials, theta functions on degenerate Riemann surfaces, Schottky relations for surfaces of special moduli, and theta functions on finite bordered Riemann surfaces.
Theta Functions, Elliptic Functions and [pi]
Author: Heng Huat Chan
Publisher: de Gruyter
Published: 2020
Total Pages: 0
ISBN-13: 9783110540710
DOWNLOAD EBOOK →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.
