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Modular Functions in Analytic Number Theory: Second Edition
 
Modular Functions in Analytic Number Theory
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-8218-4488-5
Product Code:  CHEL/337.H
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
Modular Functions in Analytic Number Theory
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Modular Functions in Analytic Number Theory: Second Edition
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-8218-4488-5
Product Code:  CHEL/337.H
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 3371993; 154 pp
    MSC: 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 Number-Theoretic 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 number-theoretic functions. However, at the heart of these particular applications to the treatment of these specific number-theoretic functions lies the general theory of automorphic functions, a theory of far-reaching 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 self-contained for those readers who have had a good first-year 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.”

  • Additional Material
     
     
  • Reviews
     
     
    • ...a systematic, self-contained 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 3371993; 154 pp
MSC: 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 Number-Theoretic 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 number-theoretic functions. However, at the heart of these particular applications to the treatment of these specific number-theoretic functions lies the general theory of automorphic functions, a theory of far-reaching 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 self-contained for those readers who have had a good first-year 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, self-contained 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.