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Some Applications of Modular Forms

£30.99

Part of Cambridge Tracts in Mathematics

  • Date Published: July 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521067706

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  • 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. In order to keep the presentation reasonably self-contained, Professor Sarnak begins by developing the necessary background material in modular forms. He then considers the solution of three problems: the Ruziewicz problem concerning finitely additive rotationally invariant measures on the sphere; the explicit construction of highly connected but sparse graphs: '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. These applications are carried out in detail. The book therefore should be accessible to a wide audience of graduate students and researchers in mathematics and computer science.

    • Based on public lectures at Yale, therefore not too technical, and of broad interest
    • Very well-known author, who was invited speaker at this year's Int Congress of Maths (all the flyers we prepared were taken)
    • Interest to number theorists and combinatorialists
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    Reviews & endorsements

    Review of the hardback: '… fascinating book …' Monatshefte für Mathematik

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    Product details

    • Date Published: July 2008
    • format: Paperback
    • isbn: 9780521067706
    • length: 124 pages
    • dimensions: 229 x 152 x 7 mm
    • weight: 0.19kg
    • contains: 7 b/w illus.
    • availability: Available
  • Table of Contents

    Introduction
    1. Modular forms
    2. Invariant means on L∞(Sn)
    3. Ramanujan graphs
    4. Bounds for Fourier coefficients of 1/2-integral weight
    Bibliogrpahy
    Index.

  • Author

    Peter Sarnak, Stanford University, California

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