A Brief Introduction To Theta Functions
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A Brief Introduction To Theta Functions
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Author : Richard Bellman
language : en
Publisher: Courier Corporation
Release Date : 2013-01-01
A Brief Introduction To Theta Functions written by Richard Bellman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Mathematics categories.
Originally published: New York: Rinehart and Winston, 1961.
Ramanujan S Theta Functions
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Author : Shaun Cooper
language : en
Publisher: Springer
Release Date : 2017-06-12
Ramanujan S Theta Functions written by Shaun Cooper and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-12 with Mathematics categories.
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.
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Author : George E. Andrews
language : en
Publisher: 清华大学出版社有限公司
Release Date : 2004
written by George E. Andrews and has been published by 清华大学出版社有限公司 this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Functions, Special categories.
Abelian Varieties Theta Functions And The Fourier Transform
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Author : Alexander Polishchuk
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-21
Abelian Varieties Theta Functions And The Fourier Transform written by Alexander Polishchuk and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-21 with Mathematics categories.
Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.
Tata Lectures On Theta I
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Author : David Mumford
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-25
Tata Lectures On Theta I written by David Mumford and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-25 with Mathematics categories.
This volume contains the first two out of four chapters which are intended to survey a large part of the theory of theta functions. These notes grew out of a series of lectures given at the Tata Institute of Fundamental Research in the period October, 1978, to March, 1979, on which notes were taken and excellently written up by C. Musili and M. Nori. I subsequently lectured at greater length on the contents of Chapter III at Harvard in the fall of 1979 and at a Summer School in Montreal in August, 1980, and again notes were very capably put together by E. Previato and M. Stillman, respectively. Both the Tata Institute and the University of Montreal publish lecture note series in which I had promised to place write-ups of my lectures there. However, as the project grew, it became clear that it was better to tie all these results together, rearranging and consolidating the material, and to make them available from one place. I am very grateful to the Tata Institute and the University of Montreal for permission to do this, and to Birkhauser-Boston for publishing the final result. The first 2 chapters study theta functions strictly from the viewpoint of classical analysis. In particular, in Chapter I, my goal was to explain in the simplest cases why the theta functions attracted attention.
Introduction To Algebraic And Abelian Functions
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 1982-12
Introduction To Algebraic And Abelian Functions written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-12 with Mathematics categories.
Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. For this revised edition, the material on theta functions has been expanded, and the example of the Fermat curves is carried throughout the text. This volume is geared toward a second-year graduate course, but it leads naturally to the study of more advanced books listed in the bibliography.
Tata Lectures On Theta Iii
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Author : David Mumford
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-22
Tata Lectures On Theta Iii written by David Mumford and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-22 with Mathematics categories.
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).
The Fourier Analytic Proof Of Quadratic Reciprocity
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Author : Michael C. Berg
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-30
The Fourier Analytic Proof Of Quadratic Reciprocity written by Michael C. Berg and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-30 with Mathematics categories.
A unique synthesis of the three existing Fourier-analytictreatments of quadratic reciprocity. The relative quadratic case was first settled by Hecke in 1923,then recast by Weil in 1964 into the language of unitary grouprepresentations. The analytic proof of the general n-th order caseis still an open problem today, going back to the end of Hecke'sfamous treatise of 1923. The Fourier-Analytic Proof of QuadraticReciprocity provides number theorists interested in analyticmethods applied to reciprocity laws with a unique opportunity toexplore the works of Hecke, Weil, and Kubota. This work brings together for the first time in a single volume thethree existing formulations of the Fourier-analytic proof ofquadratic reciprocity. It shows how Weil's groundbreakingrepresentation-theoretic treatment is in fact equivalent to Hecke'sclassical approach, then goes a step further, presenting Kubota'salgebraic reformulation of the Hecke-Weil proof. Extensivecommutative diagrams for comparing the Weil and Kubotaarchitectures are also featured. The author clearly demonstrates the value of the analytic approach,incorporating some of the most powerful tools of modern numbertheory, including adèles, metaplectric groups, andrepresentations. Finally, he points out that the critical commonfactor among the three proofs is Poisson summation, whosegeneralization may ultimately provide the resolution for Hecke'sopen problem.
Elliptic Curves
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Author : Henry McKean
language : en
Publisher: Cambridge University Press
Release Date : 1999-08-13
Elliptic Curves written by Henry McKean and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-13 with Mathematics categories.
The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This 1997 book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text.
Crc Concise Encyclopedia Of Mathematics
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Author : Eric W. Weisstein
language : en
Publisher: CRC Press
Release Date : 2002-12-12
Crc Concise Encyclopedia Of Mathematics written by Eric W. Weisstein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-12 with Mathematics categories.
Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d