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Synopsis
This thorough work presents the fundamental results of modular function theory as developed during the nineteenth and early-twentieth centuries. It features beautiful formulas and derives them using skillful and ingenious manipulations, especially classical methods often overlooked today. Starting with the work of Gauss, Abel, and Jacobi, the book then discusses the attempt by Dedekind to construct a theory of modular functions independent of elliptic functions. The latter part of the book explains how Hurwitz completed this task and includes one of Hurwitz's landmark papers, translated by the author, and delves into the work of Ramanujan, Mordell, and Hecke. For graduate students and experts in modular forms, this book demonstrates the relevance of these original sources and thereby provides the reader with new insights into contemporary work in this area.
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Book Description
Many mathematicians today believe mathematical works from past centuries are inaccessible, not useful, or both. This book demonstrates that past works are not only readable, but brimming with ideas and insights. It is aimed at graduate students or researchers working in modular functions, number theory, complex analysis, or special functions.
About the Author
Ranjan Roy is the Huffer Professor of Mathematics and Astronomy at Beloit College, Wisconsin, and has published papers in differential equations, fluid mechanics, complex analysis, and the development of mathematics. He received the Allendoerfer Prize, the Wisconsin MAA teaching award, and the MAA Haimo Award for Distinguished Mathematics Teaching, and was twice named Teacher of the Year at Beloit College. He is a co-author of three chapters in the NIST Handbook of Mathematical Functions, of Special Functions (with Andrews and Askey, Cambridge, 2010), and the author of Sources in the Development of Mathematics (Cambridge, 2011).
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- PublisherCambridge University Press
- Publication date2017
- ISBN 10 1107159385
- ISBN 13 9781107159389
- BindingHardcover
- LanguageEnglish
- Edition number1
- Number of pages488
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Hardcover. Condition: new. Hardcover. This thorough work presents the fundamental results of modular function theory as developed during the nineteenth and early-twentieth centuries. It features beautiful formulas and derives them using skillful and ingenious manipulations, especially classical methods often overlooked today. Starting with the work of Gauss, Abel, and Jacobi, the book then discusses the attempt by Dedekind to construct a theory of modular functions independent of elliptic functions. The latter part of the book explains how Hurwitz completed this task and includes one of Hurwitz's landmark papers, translated by the author, and delves into the work of Ramanujan, Mordell, and Hecke. For graduate students and experts in modular forms, this book demonstrates the relevance of these original sources and thereby provides the reader with new insights into contemporary work in this area. Many mathematicians today believe mathematical works from past centuries are inaccessible, not useful, or both. This book demonstrates that past works are not only readable, but brimming with ideas and insights. It is aimed at graduate students or researchers working in modular functions, number theory, complex analysis, or special functions. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9781107159389
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