Fonction zêta associée à la série principale sphérique de certains espaces symétriques

DOI10.24033/asens.1685zbMath0806.14039OpenAlexW2510639788MaRDI QIDQ4289253

Nicole Bopp, Hubert Rubenthaler

Publication date: 24 May 1994

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1993_4_26_6_701_0

zbMATH Keywords

symmetric spaceszeta functionprehomogeneous vector space of commutative parabolic type

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10)

Related Items (3)

Zeta distributions and boundary values of Poisson transforms ⋮ Non-parabolic prehomogeneous vector spaces and exceptional Lie algebras ⋮ Orthogonal roots, quadratic forms and orbits of simple graded Lie algebras

Cites Work

• The Capelli identity, the double commutant theorem, and multiplicity-free actions
• Vector valued invariants of prehomogeneous vector spaces
• The functional equation of zeta distributions associated with formally real Jordan algebras
• Structure of prehomogeneous spaces associated with certain graded Lie algebras
• Opérateurs différentiels de Shimura et espaces préhomogènes. (Shimura differential operators and prehomogeneous spaces)
• Meromorphic property of the functions \(P^ \lambda\)
• Zeta functions of simple algebras
• The principal series for a reductive symmetric space. I. $H$-fixed distribution vectors
• Sur les représentations induites des groupes de Lie
• A classification of irreducible prehomogeneous vector spaces and their relative invariants
• Zeta functions in several variables associated with prehomogeneous vector spaces. I: Functional equations
• On Dirichlet series whose coefficients are class numbers of integral binary cubic forms
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