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.

46 pages

References in corpus (1)

• On the Gross-Prasad conjecture with its refinement for $\left(\mathrm{SO}\left(5\right),\mathrm{SO}\left(2\right)\right)$ and the generalized Böcherer conjecture