On the Shintani zeta function for the space of binary quadratic forms

DOI10.1007/BF01444626zbMath0757.11027MaRDI QIDQ1190817

Akihiko Yukie

Publication date: 26 September 1992

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164919

zbMATH Keywords

distributionsquadratic formsprehomogeneous vector spacetest functionadelization of Shintani's zeta functionadjusted zeta functionprincipal part of the poles

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) Other Dirichlet series and zeta functions (11M41) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10)

Related Items

The Shintani double zeta functions, On Dirichlet series whose coefficients are class numbers of binary quadratic forms, The Trace Formula and Prehomogeneous Vector Spaces, Zeta Functions for the Adjoint Action of GL(n) and Density of Residues of Dedekind Zeta Functions, On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2, Prehomogeneous vector spaces and field extensions, A mean value theorem for orders of degree zero divisor class groups of quadratic extensions over a function field, On Shintani zeta functions for $\mathrm {GL}(2)$

Cites Work

• Eisenstein series of \(1\over 2\)-integral weight and the mean value of real Dirichlet L-series
• Adèles and algebraic groups. (Appendix 1: The case of the group \(G_2\), by M. Demazure. Appendix 2: A short survey of subsequent research on Tamagawa numbers, by T. Ono)
• On zeta functions associated with prehomogeneous vector spaces
• On the functional equations satisfied by Eisenstein series
• Some finiteness properties of adele groups over number fields
• Sur la formule de Siegel dans la théorie des groupes classiques
• Sur certains groupes d'opérateurs unitaires
• The average measure of quadratic forms with given determinant and signature
• The adelic zeta function associated to the space of binary cubic forms. II: Local theory.
• Density of discriminants of cubic extensions.
• On Dirichlet series whose coefficients are class numbers of integral binary cubic forms
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