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  3. Shintani Zeta Functions
  • Cited by 10
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    • Publisher:
      Cambridge University Press
      Publication date:
      March 2010
      February 1994
      ISBN:
      9780511662331
      9780521448048
      DOI:
      https://doi.org/10.1017/CBO9780511662331
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.507kg, 352 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Number Theory
      Series:
      London Mathematical Society Lecture Note Series (183)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Number Theory
    Series:
    London Mathematical Society Lecture Note Series (183)
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    Book description

    The theory of prehomogeneous vector spaces is a relatively new subject although its origin can be traced back through the works of Siegel to Gauss. The study of the zeta functions related to prehomogeneous vector spaces can yield interesting information on the asymptotic properties of associated objects, such as field extensions and ideal classes. This is amongst the first books on this topic, and represents the author's deep study of prehomogeneous vector spaces. Here the author's aim is to generalise Shintani's approach from the viewpoint of geometric invariant theory, and in some special cases he also determines not only the pole structure but also the principal part of the zeta function. This book will be of great interest to all serious workers in analytic number theory.

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