On functional equations of complex powers

DOI10.1007/BF01388789zbMath0599.12017OpenAlexW2081593158MaRDI QIDQ1080475

Jun-ichi Igusa

Publication date: 1986

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143356

zbMATH Keywords

functional equationstempered distributionslocal fieldquasi-charactersprehomogeneous vector spaceb-functioncomplex powersp-adic fieldszeta distributionsSchwartz-Bruhat functions\(\Gamma \) -matrixconnected reductive algebraic K-subgroupmeromorphic continuations

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Group actions on varieties or schemes (quotients) (14L30) Integral transforms in distribution spaces (46F12) Functional equations for functions with more general domains and/or ranges (39B52) Representations of Lie and linear algebraic groups over local fields (22E50) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Zeta functions and (L)-functions (11S40)

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Universal transitivity of simple and 2-simple prehomogeneous vector spaces ⋮ On Dirichlet series whose coefficients are class numbers of binary quadratic forms ⋮ On a certain class of prehomogeneous vector spaces ⋮ Twists of the Iwasawa-Tate zeta function ⋮ Degenerate principal series representations for \(U(n,n)\) ⋮ Period of the Ikeda type lift for the exceptional group of type \(E_{7,3}\) ⋮ Universal transitivity of reductive prehomogeneous vector spaces with a finite number of orbits ⋮ Siegel series for skew Hermitian forms over quaternion algebras ⋮ Degenerate principal series representations for quaternionic unitary groups ⋮ The local zeta function for the non-trivial characters associated with the singular Jordan algebras ⋮ Motivic zeta functions for prehomogeneous vector spaces and castling transformations ⋮ Orthogonal roots, quadratic forms and orbits of simple graded Lie algebras

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