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  3. Modular Forms and Functions
  • Cited by 206
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2010
      September 1977
      ISBN:
      9780511566035
      9780521091688
      DOI:
      https://doi.org/10.1017/CBO9780511566035
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.59kg, 400 Pages
      • Subjects:
      Mathematics, Number Theory
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    Subjects:
    Mathematics, Number Theory
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    Book description

    This book provides an introduction to the theory of elliptic modular functions and forms, a subject of increasing interest because of its connexions with the theory of elliptic curves. Modular forms are generalisations of functions like theta functions. They can be expressed as Fourier series, and the Fourier coefficients frequently possess multiplicative properties which lead to a correspondence between modular forms and Dirichlet series having Euler products. The Fourier coefficients also arise in certain representational problems in the theory of numbers, for example in the study of the number of ways in which a positive integer may be expressed as a sum of a given number of squares. The treatment of the theory presented here is fuller than is customary in a textbook on automorphic or modular forms, since it is not confined solely to modular forms of integral weight (dimension). It will be of interest to professional mathematicians as well as senior undergraduate and graduate students in pure mathematics.

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