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Shintani Zeta Functions

Shintani Zeta Functions

Part of London Mathematical Society Lecture Note Series

  • Date Published: February 1994
  • availability: Available
  • format: Paperback
  • isbn: 9780521448048


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About the Authors
  • 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.

    • Only comprehensive book on this subject
    • Author is the prime mover behind the development of the subject
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    Product details

    • Date Published: February 1994
    • format: Paperback
    • isbn: 9780521448048
    • length: 352 pages
    • dimensions: 228 x 152 x 20 mm
    • weight: 0.507kg
    • availability: Available
  • Table of Contents

    1. The general theory
    2. Eisenstein series
    3. The general program
    4. The zeta function for the spaces
    5. The case G=GL(2)¥GL(2), V=Sym2 k2ƒk2
    6. The case G=GL(2)¥GL(1)2, V=Sym2 k2ƒk
    7. The case G=GL(2)¥GL(1), V=Sym2 k2ƒk2
    8. Invariant theory of pairs of ternary quadratic forms
    9. Preliminary estimates
    10. The non-constant terms associated with unstable strata
    11. Unstable distributions
    12. Contributions from unstable strata
    13. The main theorem.

  • Author

    Akihiko Yukie, Oklahoma State University

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