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

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.

arXiv comment46 pages

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