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Some Applications of Modular Forms

Part of Cambridge Tracts in Mathematics

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


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About the Authors
  • 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.

    • 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

    "...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

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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

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

  • Author

    Peter Sarnak, Stanford University, California

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