Elliptic and Modular Functions from Gauss to Dedekind to Hecke 1st Edition by Ranjan Roy (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book on the “Elliptic and modular Functions – from Gauss to Dedekind to Hecke” is another gem from the Author of the uniquely exhaustive “Sources in the development of Mathematics – series and products from the Fifteenth to the Twenty-first century”, and in the same tradition of historical and detailed development of important topics in pure mathematics from their original sources as they were discovered by the great Geniuses of the past. The treatment in Ranjan Roy’s book brings LIFE into the subject, makes it lively, lovely and eminently digestible; and gives you ample insight into why something developed the way it did, and the personality that created it, allowing you to dare to bond with the Genius. What a wonderful of learning mathematics! You not only appreciate the topic but the topic-maker as well! The subject is no longer a mere dry set of symbols and formulations, but a topic with a well-deserved place in History. For example, one may know about elliptic functions, and still not be aware of the contributions of Abel and Jacobi as has been beautifully brought out in considerable detail in chaper 3.Ranjan Roy has clearly demonstrated that the treatment of an important but difficult topic in pure mathematics from an historical and their sources perspective can still be a full treatment of it – complete with all the equations, definitions, theorems and EXERCISES – like an advanced text book. It is my contention that such a treatment is far more profitable for the serious student than a conventional textbook.This book is a very serious book written by a very competent mathematician; and not just a popular mathematics or science book written by a science -journalist for making money who is afraid of writing equations in the language of mathematics either because of inability to understand them or being afraid the book might not sell in huge numbers i.e. to general public.I am enjoying this book immensely, and grateful for the service being done by Ranjan Roy in the propagation of Pure mathematics. Let me wish for more books like this from RR.

⭐You need to be a mathematician to appreciate this book, and it helps to know some analytic number theory, but if you have this background, this is an immensely scholarly and readable history of the development of a central field of mathematics, from the early work of Gauss in 1808 to the work of Hardy, Mordell and Hecke in the first quarter of the 20th century. In the tradition of Roy’s earlier”Special Functions” (with George Andrews and Richard Askey) and “Sources in the Development of Mathematics,” careful attention is paid to the original techniques of the pioneers, so that we can appreciate their ingenuity, and even modern experts will find much to learn and admire.

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