Shintani function and its application to automorphic \(L\)-functions for classical groups. I: The case of orthogonal groups

DOI10.1007/BF01459771zbMath0813.11032OpenAlexW1250622352MaRDI QIDQ1327092

Atsushi Murase, Takashi Sugano

Publication date: 11 July 1994

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

Full work available at URL: https://eudml.org/doc/165197

zbMATH Keywords

functional equationorthogonal groupautomorphic \(L\)-functionsautomorphic formpolesShintani functionRankin-Selberg type zeta-integral

Mathematics Subject Classification ID

Other groups and their modular and automorphic forms (several variables) (11F55) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66)

Related Items (16)

Spectral square means for period integrals of wave functions on real hyperbolic spaces ⋮ On standard L-functions attached to automorphic forms on definite orthogonal groups ⋮ Unramified Godement-Jacquet theory for the spin similitude group ⋮ Unnamed Item ⋮ Shintani functions and automorphic \(L\)-functions for \(GL(n)\) ⋮ An explicit formula of the unramified Shintani functions for \((\mathbf{GSp}_4, \mathbf{GL}_2 \times_{\mathbf{GL}_1} \mathbf{GL}_2)\) ⋮ An explicit formula of the unramified Shintani functions for \((\mathbf{GSp}_4,\mathbf{GL}_2 \times_{\mathbf{GL}_1}\mathbf{GL}_2)\) and its application ⋮ Shintani functions on $GL(2,{\mathbf {C}})$ ⋮ Spectral average of central values of automorphic \(L\)-functions for holomorphic cusp forms on \(\mathrm{SO}_0(m,2)\). I ⋮ Whittaker-Shintani function for orthogonal groups ⋮ Spinor $L$-functions for generic cusp forms on $GSp(2)$ belonging to principal series representations ⋮ A spectral identity for second moments of Eisenstein series of \(\mathrm{O}(n,1)\) ⋮ Shintani functions on $GL(2,\mathbf {R})$ ⋮ Certain Rankin-Selberg integral for unitary groups ⋮ Relation of orbital integrals on \(SO(5)\) and \(PGL(2)\) ⋮ Shintani functions on \(\mathrm{SL}(3,\mathbb R)\)

Cites Work

• Explicit constructions of automorphic \(L\)-functions
• Ein Rationalitätssatz für formale Heckereihen zur Siegelschen Modulgruppe. (A rationality theorem for formal Hecke series related to the Siegel modular group)
• On the functional equations satisfied by Eisenstein series
• Theory of spherical functions on reductive algebraic groups over p-adic fields
• 𝐿 functions for the group 𝐺₂
• ε factor of representations of classical groups
• On L-functions for GSp(4) X GL(2) and their special values.
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