Hardcover ISBN:  9780821844885 
Product Code:  CHEL/337.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
Hardcover ISBN:  9780821844885 
Product Code:  CHEL/337.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 

Book DetailsAMS Chelsea PublishingVolume: 337; 1993; 154 ppMSC: Primary 11;
From the Preface: “An accurate (though uninspiring) title for this book would have been Applications of the Theory of the Modular Forms \(\eta(\tau)\) and \(\vartheta(\tau)M\) to the NumberTheoretic functions \(p(n)\) and \(r_s(n)\) respectively. This is accurate because, except in the first two chapters, we deal exclusively with these two modular forms and these two numbertheoretic functions. However, at the heart of these particular applications to the treatment of these specific numbertheoretic functions lies the general theory of automorphic functions, a theory of farreaching significance with important connections to a great many fields of mathematics. Indeed, together with Riemann surface theory, analytic number theory has provided the principal impetus for the development over the last century of the theory of automorphic functions ... I have tried to keep the book selfcontained for those readers who have had a good firstyear graduate course in analysis; and, in particular, I have assumed readers to be familiar with the Cauchy theory and the Lebesgue theorem of dominated convergence.”

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...a systematic, selfcontained and very well written exposition of a beautiful chapter of analytic number theory... All told, this is a very pleasing addition to the bookshelf of a number theorist.
Mathematical Reviews


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From the Preface: “An accurate (though uninspiring) title for this book would have been Applications of the Theory of the Modular Forms \(\eta(\tau)\) and \(\vartheta(\tau)M\) to the NumberTheoretic functions \(p(n)\) and \(r_s(n)\) respectively. This is accurate because, except in the first two chapters, we deal exclusively with these two modular forms and these two numbertheoretic functions. However, at the heart of these particular applications to the treatment of these specific numbertheoretic functions lies the general theory of automorphic functions, a theory of farreaching significance with important connections to a great many fields of mathematics. Indeed, together with Riemann surface theory, analytic number theory has provided the principal impetus for the development over the last century of the theory of automorphic functions ... I have tried to keep the book selfcontained for those readers who have had a good firstyear graduate course in analysis; and, in particular, I have assumed readers to be familiar with the Cauchy theory and the Lebesgue theorem of dominated convergence.”

...a systematic, selfcontained and very well written exposition of a beautiful chapter of analytic number theory... All told, this is a very pleasing addition to the bookshelf of a number theorist.
Mathematical Reviews