Spherical functions and local densities on the space of p-adic quaternion Hermitian forms

DOI10.1142/S1793042122500324zbMath1483.11110arXiv2001.04636OpenAlexW3199582518MaRDI QIDQ5069079

Yumiko Hironaka

Publication date: 8 April 2022

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

Full work available at URL: https://arxiv.org/abs/2001.04636

zbMATH Keywords

orthogonal polynomialsPlancherel formulaspherical functionquaternion Hermitian forms

Mathematics Subject Classification ID

(p)-adic theory, local fields (11F85) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) (p)-adic theory (11E95)

Uses Software

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Cites Work

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• Spherical functions of Hermitian and symmetric forms. III
• Local zeta functions on Hermitian forms and its application to local densities
• Spherical functions and local densities on Hermitian forms
• Orthogonal polynomials associated with root systems
• Harmonic analysis on the space of \(p\)-adic unitary Hermitian matrices, mainly for dyadic case
• Local densities of alternating forms
• Spherical functions on $p$-adic homogeneous spaces
• A note on local densities of quadratic forms
• Spherical Functions and Local Densities of Alternating Forms
• Representations of quadratic forms and their application to Selberg’s zeta functions
• Spherical functions on the space of $p$-adic unitary hermitian matrices II, the case of odd size
• SPHERICAL FUNCTIONS ON THE SPACE OF p-ADIC UNITARY HERMITIAN MATRICES

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