Spherical functions and local densities on hermitian forms Dedicated to Professor Ichiro Satake on his seventieth birthday

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概要

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• First we give a formula of spherical functions on certain spherical homogeneous spaces. Then, applying it, we complete the theory of the spherical functions on the space X of nondegenerate unramified hermitian forms on a \mathfrak{p}-adic number field. More precisely, we give an explicit expression for the spherical functions, prove theorems on the spherical Fourier transforms on the space of Schwartz-Bruhat functions on X, and parametrize of all spherical functions on X. Finally, as an application, we give explicit expressions of local densities of representations of hermitian forms.

• 社団法人 日本数学会の論文

著者

• Hironaka Yumiko

  Department Of Mathematics Faculty Of Science Shinshu University

関連論文

• On the Galois groups of the Maximal p-extensions of Algebraic Number Fields
• Fourier-Eisenstein transform and plancherel formula for rational binary quadratic forms
• Spherical functions of hermitian and symmetric forms, III
• Spherical functions and local densities on hermitian forms Dedicated to Professor Ichiro Satake on his seventieth birthday
• Finite groups with trivial class groups
• Spherical functions of hermitian and symmetric forms II

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