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arXiv · 2106.16076

On some zeta-integrals for unramified representations of GSp(4)

David Loeffler
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Abstract

This article is a companion to several works of the author and others on the arithmetic of automorphic forms for GSp(4), and their associated L-functions and Galois representations. These works require, at various points, an input from smooth representation theory over p-adic local fields: the computation of values of the unique trilinear form on an unramified representation of GSp(4) x GL(2) x GL(2) invariant under the diagonal GL(2) x GL(2), for various different input data. In this note, we carry out these local computations, using a general formula for Shintani functions due to Gejima.

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David Loeffler. 2021-06-30. On some zeta-integrals for unramified representations of GSp(4). https://arxiv.org/abs/2106.16076

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