Jacobian Theta Functions And Differential Equations
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| Author | : David Mumford |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 285 |
| Release | : 2012-04-15 |
| Genre | : Mathematics |
| ISBN | : 0817645780 |
The second in a series of three volumes that survey the theory of theta functions, this volume emphasizes the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics. It presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a self-contained introduction to the theory of the Jacobians. It also ties together nineteenth-century discoveries due to Jacobi, Neumann, and Frobenius with recent discoveries of Gelfand, McKean, Moser, John Fay, and others.
| Author | : David Mumford |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 210 |
| Release | : 2010-10-22 |
| Genre | : Mathematics |
| ISBN | : 0817645799 |
This volume is the third 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).
| Author | : David Mumford |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 248 |
| Release | : 2007-06-25 |
| Genre | : Mathematics |
| ISBN | : 0817645772 |
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).
| Author | : |
| Publisher | : |
| Total Pages | : 272 |
| Release | : 1984 |
| Genre | : |
| ISBN | : 9783764331108 |
| Author | : David Mumford |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 251 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 148992843X |
The first of a series of three volumes surveying the theory of theta functions and its significance in the fields of representation theory and algebraic geometry, this volume deals with the basic theory of theta functions in one and several variables, and some of its number theoretic applications. Requiring no background in advanced algebraic geometry, the text serves as a modern introduction to the subject.
| Author | : Richard Bellman |
| Publisher | : Courier Corporation |
| Total Pages | : 100 |
| Release | : 2013-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486492958 |
Originally published: New York: Rinehart and Winston, 1961.
| Author | : Shaun Cooper |
| Publisher | : Springer |
| Total Pages | : 696 |
| Release | : 2017-06-12 |
| Genre | : Mathematics |
| ISBN | : 3319561723 |
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 | : Edmund Taylor Whittaker |
| Publisher | : |
| Total Pages | : 638 |
| Release | : 1920 |
| Genre | : Analytic functions |
| ISBN | : |
| Author | : Komaravolu Chandrasekharan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 199 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642522440 |
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 | : Masaki Kashiwara |
| Publisher | : Academic Press |
| Total Pages | : 501 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483267946 |
Algebraic Analysis: Papers Dedicated to Professor Mikio Sato on the Occasion of his 60th Birthday, Volume II is a collection of research papers on algebraic analysis and related topics in honor to Professor Mikio Sato’s 60th birthday. This volume is divided into 29 chapters and starts with research works concerning the fundamentals of KP equations, strings, Schottky problem, and the applications of transformation theory for nonlinear integrable systems to linear prediction problems and isospectral deformations,. The subsequent chapters contain papers on the approach to nonlinear integrable systems, the Hodge numbers, the stochastic different equation for the multi-dimensional weakly stationary process, and a method of harmonic analysis on semisimple symmetric spaces. These topics are followed by studies on the quantization of extended vortices, moduli space for Fuchsian groups, microfunctions for boundary value problems, and the issues of multi-dimensional integrable systems. The remaining chapters explore the practical aspects of pseudodifferential operators in hyperfunction theory, the elliptic solitons, and Carlson’s theorem for holomorphic functions. This book will prove useful to mathematicians and advance mathematics students.
