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arXiv · 2407.05583

The Ranking-Selberg integral on ${\bf GSp(2)}$ for square free levels

Seiji Kuga·Masao Tsuzuki
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Abstract

We explicitly compute the Rankin-Selberg type integral introduced by Piatetski-Shapiro over adeles for vector-valued Siegel cusp forms of square-free levels $\Gamma_0(N)$. On the way, for particular test functions in the Bessel models of irreducible admissible representations, exact evaluations of the local zeta-integrals are given.

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Seiji Kuga, Masao Tsuzuki. 2024-07-08. The Ranking-Selberg integral on ${\bf GSp(2)}$ for square free levels. https://doi.org/10.2140/pjm.2026.342.299

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