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Theta Functions
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Download or read book Theta Functions written by Jun-ichi Igusa and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis A Brief Introduction to Theta Functions by : Richard Bellman
Download or read book A Brief Introduction to Theta Functions written by Richard Bellman and published by Courier Corporation. This book was released on 2013-01-01 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: New York: Rinehart and Winston, 1961.
Book Synopsis Theta Functions on Riemann Surfaces by : J. D. Fay
Download or read book Theta Functions on Riemann Surfaces written by J. D. Fay and published by Springer. This book was released on 2006-11-15 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Ramanujan's Theta Functions by : Shaun Cooper
Download or read book Ramanujan's Theta Functions written by Shaun Cooper and published by Springer. This book was released on 2017-06-12 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Abelian Varieties, Theta Functions and the Fourier Transform by : Alexander Polishchuk
Download or read book Abelian Varieties, Theta Functions and the Fourier Transform written by Alexander Polishchuk and published by Cambridge University Press. This book was released on 2003-04-21 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.
Book Synopsis Theta Functions by : Maruti Ram Murty
Download or read book Theta Functions written by Maruti Ram Murty and published by American Mathematical Soc.. This book was released on 1993-01-01 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Conformal Blocks, Generalized Theta Functions and the Verlinde Formula by : Shrawan Kumar
Download or read book Conformal Blocks, Generalized Theta Functions and the Verlinde Formula written by Shrawan Kumar and published by Cambridge University Press. This book was released on 2021-11-25 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a complete proof of the Verlinde formula and of its connection to generalized theta functions.
Book Synopsis Theta Functions, Elliptic Functions and [pi] by : Heng Huat Chan
Download or read book Theta Functions, Elliptic Functions and [pi] written by Heng Huat Chan and published by de Gruyter. This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Eta Products and Theta Series Identities by : Günter Köhler
Download or read book Eta Products and Theta Series Identities written by Günter Köhler and published by Springer Science & Business Media. This book was released on 2011-01-15 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with products of Dedekind's eta function, with Hecke theta series on quadratic number fields, and with Eisenstein series. The author brings to the public the large number of identities that have been discovered over the past 20 years, the majority of which have not been published elsewhere. The book will be of interest to graduate students and scholars in the field of number theory and, in particular, modular forms. It is not an introductory text in this field. Nevertheless, some theoretical background material is presented that is important for understanding the examples in Part II of the book. In Part I relevant definitions and essential theorems -- such as a complete proof of the structure theorems for coprime residue class groups in quadratic number fields that are not easily accessible in the literature -- are provided. Another example is a thorough description of an algorithm for listing all eta products of given weight and level, together with proofs of some results on the bijection between these eta products and lattice simplices.
Book Synopsis Algebraic Geometry and Theta Functions by : Arthur B. Coble
Download or read book Algebraic Geometry and Theta Functions written by Arthur B. Coble and published by American Mathematical Soc.. This book was released on 1929-12-31 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Tata Lectures on Theta I by : David Mumford
Download or read book Tata Lectures on Theta I written by David Mumford and published by Springer Science & Business Media. This book was released on 2007-06-25 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Book Synopsis Theta functions, elliptic functions and π by : Heng Huat Chan
Download or read book Theta functions, elliptic functions and π written by Heng Huat Chan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-07-06 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theta Functions and Knots by : R?zvan Gelca
Download or read book Theta Functions and Knots written by R?zvan Gelca and published by World Scientific. This book was released on 2014 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the relationship between classical theta functions and knots. It is based on a novel idea of Razvan Gelca and Alejandro Uribe, which converts Weil''s representation of the Heisenberg group on theta functions to a knot theoretical framework, by giving a topological interpretation to a certain induced representation. It also explains how the discrete Fourier transform can be related to 3- and 4-dimensional topology. Theta Functions and Knots can be read in two perspectives. People with an interest in theta functions or knot theory can learn how the two are related. Those interested in ChernOCoSimons theory find here an introduction using the simplest case, that of abelian ChernOCoSimons theory. Moreover, the construction of abelian ChernOCoSimons theory is based entirely on quantum mechanics, and not on quantum field theory as it is usually done. Both the theory of theta functions and low dimensional topology are presented in detail, in order to underline how deep the connection between these two fundamental mathematical subjects is. Hence the book is a self-contained, unified presentation. It is suitable for an advanced graduate course, as well as for self-study. Contents: Some Historical Facts; A Quantum Mechanical Prototype; Surfaces and Curves; The Theta Functions Associated to a Riemann Surface; From Theta Functions to Knots; Some Results About 3- and 4-Dimensional Manifolds; The Discrete Fourier Transform and Topological Quantum Field Theory; Theta Functions and Quantum Groups; An Epilogue OCo Abelian ChernOCoSimons Theory. Readership: Graduate students and young researchers with an interest in complex analysis, mathematical physics, algebra geometry and low dimensional topology.
Book Synopsis Cubic Metaplectic Forms and Theta Functions by : Nikolai Proskurin
Download or read book Cubic Metaplectic Forms and Theta Functions written by Nikolai Proskurin and published by Springer. This book was released on 2006-11-14 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an introduction to the theory of cubic metaplectic forms on the 3-dimensional hyperbolic space and the author's research on cubic metaplectic forms on special linear and symplectic groups of rank 2. The topics include: Kubota and Bass-Milnor-Serre homomorphisms, cubic metaplectic Eisenstein series, cubic theta functions, Whittaker functions. A special method is developed and applied to find Fourier coefficients of the Eisenstein series and cubic theta functions. The book is intended for readers, with beginning graduate-level background, interested in further research in the theory of metaplectic forms and in possible applications.
Book Synopsis Theta Functions-Bowdoin 1987, Part 2 by : Leon Ehrenpreis
Download or read book Theta Functions-Bowdoin 1987, Part 2 written by Leon Ehrenpreis and published by American Mathematical Soc.. This book was released on 1989 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theta Functions, Bowdoin 1987 by : Leon Ehrenpreis
Download or read book Theta Functions, Bowdoin 1987 written by Leon Ehrenpreis and published by American Mathematical Soc.. This book was released on 1989 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: During his long and productive career, Salomon Bochner worked in a variety of different areas of mathematics. This four part set brings together his collected papers, illustrating the range and depth of his mathematical interests. The books are available either individually or as a set.
Book Synopsis Theta Functions on Varieties with Effective Anti-Canonical Class by : Mark Gross
Download or read book Theta Functions on Varieties with Effective Anti-Canonical Class written by Mark Gross and published by American Mathematical Society. This book was released on 2022-07-18 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
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