The theory of modular forms and especially the so-called Ramanujan Conjectures have recently been applied to resolve problems in combinatorics, computer science, analysis, and number theory. Professor Sarnak begins by developing the necessary background material in modular forms. He then considers in detail the solution of three problems: the Rusiewisz problem concerning finitely additive rotationally invariant measures on the sphere; the explicit construction of highly connected but sparse graphs, e.g. expander graphs and Ramanujan graphs; and the Linnik problem concerning the distribution of integers that represent a given large integer as a sum of three squares.
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"...treats in detail a remarkable range of ideas and beautiful mathematics. It is highly recommended to everyone interested in modular forms." Solomon Friedberg, Mathematical Reviews
Book Description
The theory of modular forms and especially the so-called 'Ramanujan Conjectures' have been applied to resolve problems in combinatorics, computer science, analysis and number theory. This tract, based on the Wittemore Lectures given at Yale University, is concerned with describing some of these applications.
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First Sentence:
The first was proved by Mordell [Mo] and marked the beginning of Hecke's theory of Hecke operators [H]. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
large chromatic number, half integral weight, cusp form, invariant mean, automorphic forms, congruence subgroup, large girth, modular forms, theta functions New!
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The first was proved by Mordell [Mo] and marked the beginning of Hecke's theory of Hecke operators [H]. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
large chromatic number, half integral weight, cusp form, invariant mean, automorphic forms, congruence subgroup, large girth, modular forms, theta functions New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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This book cites 3
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16
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- Number Theory: An approach through history from Hammurapi to Legendre by André Weil in Back Matter (1), and Back Matter (2)
- Multiplicative Number Theory by Harold Davenport in Back Matter
- Random Graphs (Cambridge Studies in Advanced Mathematics) by Béla Bollobás in Back Matter
- Random Walks and Geometry: Proceedings of a Workshop at the Erwin Schrodinger Institute, Vienna, June 18-July 13, 2001 (De Gruyter Proceedings in Mathematics) by Vadim A. Kaimanovich on page 139, and page 179
- Emerging Applications of Number Theory (The IMA Volumes in Mathematics and its Applications) by Dennis A. Hejhal on page 386, and Back Matter
- Geometric Aspects of Functional Analysis: Israel Seminar 2002-2003 (Lecture Notes in Mathematics) by Vitali D. Milman on page 275
- Fourier Analysis on Finite Groups and Applications (London Mathematical Society Student Texts) by Audrey Terras in Back Matter
- Gauss and Jacobi Sums (Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts) by Bruce C. Berndt in Back Matter
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