L-Functions for SOn x GLk.

DOI10.1515/crll.1990.405.156zbMath0684.22009OpenAlexW3170346165MaRDI QIDQ4734038

David Ginzburg

Publication date: 1990

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/153215

zbMATH Keywords

Eisenstein seriesRankin-Selberg integralsconnected reductive algebraic groupstandard representationLanglands' conjectureautomorphic cuspidal representationunramified local integrals

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Zeta functions and (L)-functions of number fields (11R42) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55) Langlands-Weil conjectures, nonabelian class field theory (11R39)

Related Items (22)

Poles of \(L\)-functions, periods and unitary theta. I: Odd to even ⋮ On the Langlands parameter of a simple supercuspidal representation: even orthogonal groups ⋮ Theta distinguished representations, inflation and the symmetric square \(L\)-function ⋮ Archimedean zeta integrals on \(\mathrm{GL}_n\times\mathrm{GL}_m\) and \(\mathrm{SO}_{2n+1}\times\mathrm{GL}_m\) ⋮ On the Langlands parameter of a simple supercuspidal representation: odd orthogonal groups ⋮ Rankin-Selberg integrals for \(\operatorname{SO}_{2n+1}{\times}\operatorname{GL}_r\) attached to newforms and oldforms ⋮ A tower of theta correspondences for \(G_ 2\) ⋮ Multiplicativity of the gamma factors of Rankin-Selberg integrals for \(\mathrm{SO} _{2l} \times\mathrm{GL}_n\) ⋮ The unramified computation of Rankin-Selberg integrals expressed in terms of Bessel models for split orthogonal groups. I ⋮ An asymptotic expansion of \((k, c)\)-functions for \(\mathrm{GL}_n (F)\) ⋮ The unramified computation of Rankin-Selberg integrals expressed in terms of Bessel models for split orthogonal groups. II ⋮ Complementary results on the Rankin-Selberg gamma factors of classical groups ⋮ Endoscopic lifting in classical groups and poles of tensor \(L\)-functions ⋮ Whittaker-orthogonal models, functoriality, and the Rankin-Selberg method ⋮ On the standard \(L\)-function for \(G_ 2\) ⋮ An invariant theory approach for the unramified computation of Rankin-Selberg integrals for quasi-split \(\text{SO}_{2n} \times \text{GL}_n\) ⋮ Lifting automorphic representations on the double covers of orthogonal groups ⋮ Spinor L-functions, theta correspondence, and Bessel coefficients ⋮ The Langlands parameter of a simple supercuspidal representation: symplectic groups ⋮ Dimensions of Automorphic Representations, L-Functions and Liftings ⋮ Doubling constructions and tensor product \(L\)-functions: the linear case ⋮ $L$-functions for symplectic groups

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