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  3. Some Applications of Modular Forms
  • Cited by 127
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    • Publisher:
      Cambridge University Press
      Publication date:
      05 February 2012
      15 November 1990
      ISBN:
      9780511895593
      9780521402453
      9780521067706
      DOI:
      https://doi.org/10.1017/CBO9780511895593
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.345kg, 124 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.19kg, 124 Pages
      • Subjects:
      Mathematics (general), Mathematics, Number Theory, Discrete Mathematics Information Theory and Coding
      Series:
      Cambridge Tracts in Mathematics (99)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Discrete Mathematics Information Theory and Coding
    Series:
    Cambridge Tracts in Mathematics (99)
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    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. 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.

    Reviews

    Review of the hardback:‘… fascinating book …’

    Source: Monatshefte für Mathematik

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