This research computes the Rankin-Selberg integral, evaluating local zeta integrals for vector-valued forms, indicating deeper links in number theory.
We explicitly compute the Rankin-Selberg type integral introduced by Piatetski-Shapiro over adeles for vector-valued Siegel cusp forms of squarefree levels 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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Kuga et al. (2026) studied this question.
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