Spherical functions on $U(n,n)/(U(n) \times U(n))$ and hermitian Siegel series

Details Spherical functions on $U(n,n)/(U(n) \times U(n))$ and hermitian Siegel series Spherical functions on $U(n,n)/(U(n) \times U(n))$ and hermitian Siegel series

2009-04-28

arxiv.org/abs/0904.4304v3

Mathematics

Number Theory

33pages

Scientific paper

We study spherical functions on the space isomorphic to $U(2n)/(U(n)\times
U(n))$ over a $p$-adic field; those functional equations with respect to the
action of the Weyl group, the location of possible poles and zeros, explicit
formulas, and spherical Fourier transforms. Then, as an application, we give a
functional equation of $p$-adic local hermitian Siegel series.

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