Spherical functions on \(\text{Sp}_2\) as a spherical homogeneous \(\text{Sp}_2\times (\text{Sp}_1)^2\)-space

DOI10.1016/J.JNT.2004.08.012zbMath1071.22021OpenAlexW2046366082MaRDI QIDQ557563

Yumiko Hironaka

Publication date: 30 June 2005

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2004.08.012

zbMATH Keywords

eigenfunctionHaar measurespherical function\(p\)-adic fieldspecial functionspherical homogeneous space

Mathematics Subject Classification ID

(p)-adic theory, local fields (11F85) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Harmonic analysis and spherical functions (43A90) (p)-adic theory (11E95)

Related Items (3)

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 ⋮ Functional equations of spherical functions on \(p\)-adic homogeneous spaces

Cites Work

• Spherical functions of Hermitian and symmetric forms. III
• On eigenspaces of the Hecke algebra with respect to a good maximal compact subgroup of a p-adic reductive group
• Local zeta functions on Hermitian forms and its application to local densities
• Spherical functions and local densities on Hermitian forms
• Whittaker-Shintani function for orthogonal groups
• Local densities of alternating forms
• Spherical Functions and Local Densities of Alternating Forms
• On the Decomposition of a Representation of SO_n When Restricted to SO_n-1
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