Zeta integrals, Schwartz spaces and local functional equations

DOI10.1007/978-3-030-01288-5zbMath1425.11001arXiv1508.05594OpenAlexW1952613075MaRDI QIDQ1991078

Wen-Wei Li

Publication date: 29 October 2018

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.05594

zbMATH Keywords

prehomogeneous vector spaceszeta integralsperiod integralsSchwartz spaces$L$-monoidsGodement-Jacquet theory

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) Other Dirichlet series and zeta functions (11M41) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Prehomogeneous vector spaces (11S90) Zeta functions and (L)-functions (11S40)

Related Items (12)

Subconvexity of Shintani’s zeta function ⋮ On the resolution of reductive monoids and multiplicativity of \(\gamma \)-factors ⋮ On the regularity of \(D\)-modules generated by relative characters ⋮ Harmonic Analysis and Gamma Functions on Symplectic Groups ⋮ Functional equations and gamma factors of local zeta functions for the metaplectic cover of \(\mathrm{SL}_2\) ⋮ On the direct integral decomposition in branching laws for real reductive groups ⋮ A summation formula for triples of quadratic spaces ⋮ Variations on themes of Sato: a survey ⋮ A refined Poisson summation formula for certain Braverman-Kazhdan spaces ⋮ Plancherel formula for \(\mathrm{GL}_n(F)\setminus \mathrm{GL}_n(E)\) and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups ⋮ Hankel transform, Langlands functoriality and functional equation of automorphic \(L\)-functions ⋮ GENERALIZED ZETA INTEGRALS ON CERTAIN REAL PREHOMOGENEOUS VECTOR SPACES

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