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."
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Modular Forms,
This review is from: Modular Functions in Analytic Number Theory: Second Edition (Hardcover)
This is a wonderful book. I have had Dr. Knopp as a proffesor and he is an amazing mathematicain. I highly recommend this book to any student interested in Modular forms. There are many good equlities with proofs.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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modular function with respect, entire modular form, parabolic points, branch convention, multiplier system, distinct modulo, coset decomposition, modular functions, cusp form, proposed formula Key Phrases - Capitalized Phrases (CAPs): (learn more)
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
modular function with respect, entire modular form, parabolic points, branch convention, multiplier system, distinct modulo, coset decomposition, modular functions, cusp form, proposed formula Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Proof Let New!
Books on Related Topics Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
17
books
cite this book:
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- The Theory of Partitions (Encyclopedia of Mathematics and its Applications) by George E. Andrews on 4 pages
- Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics (Developments in Mathematics) by Frank G. Garvan on page 71, page 77, and page 187
- Integer Partitions by George E. Andrews on page 122, and Back Matter
- Ramanujan's Notebooks: Part IV by Bruce C. Berndt in Back Matter
- Analytic and Elementary Number Theory: A Tribute to Mathematical Legend Paul Erdos (Developments in Mathematics) by Krishnaswami Alladi on page 267
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