Spinor $L$-functions for generic cusp forms on $GSp(2)$ belonging to principal series representations

DOI10.1090/S0002-9947-08-04724-7zbMath1162.11027OpenAlexW2011465380MaRDI QIDQ3532540

Taku Ishii, Tomonori Moriyama

Publication date: 28 October 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-08-04724-7

zbMATH Keywords

spinor \(L\)-functionsWhittaker functionsprincipal seriesGSp(4)GSp(2)Novodvorsky's zeta integrals

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (7)

Whittaker functions for generalized principal series representations of \(\mathrm{GSp}(2,\mathbb{R})\) ⋮ Archimedean zeta integrals on \(\mathrm{GL}_n\times\mathrm{GL}_m\) and \(\mathrm{SO}_{2n+1}\times\mathrm{GL}_m\) ⋮ Whittaker functions for \(P_J\)-principal series representations of \(\text{Sp}(3,\mathbb R)\) ⋮ The computation of multivariate archimedean zeta integrals on ${GL}_2 \times {GSp}_4$ and ${GL}_4$ ⋮ On Petersson norms of generic cusp forms and special values of adjoint L -functions for GSp4 ⋮ Generalized Whittaker functions on \(\text{GSp}(2, \mathbb R)\) associated with indefinite quadratic forms ⋮ Principal series Whittaker functions on \(Sp(2,\mathbb{C})\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A certain Dirichlet series attached to Siegel modular forms of degree two
• Whittaker vectors and conical vectors
• Gelfand-Kirillov dimension for Harish-Chandra modules
• On Whittaker vectors and representation theory
• Principal series Whittaker functions on \(\operatorname {Sp}(2;\mathbb{R})\). II
• Shintani function and its application to automorphic \(L\)-functions for classical groups. I: The case of orthogonal groups
• Andrianov's \(L\)-functions associated to Siegel wave forms of degree two
• Commutation relations of differential operators and Whittaker functions on \(\text{Sp}_ 2(\mathbb{R})\)
• Automorphic forms on semisimple Lie groups. Notes by J. G. M. Mars.
• On principal series Whittaker functions on \(\text{Sp}(2,\mathbb R)\)
• L - functions for the p-adic group GSp (4)
• Entireness of the Spinor L-functions for certain generic cusp forms on GSp(2)
• Spinor L-functions, theta correspondence, and Bessel coefficients
• Generic transfer from GSp(4) to GL(4)
• Fonctions de Whittaker associées aux groupes de Chevalley

This page was built for publication: Spinor $L$-functions for generic cusp forms on $GSp(2)$ belonging to principal series representations