The Rankin–Selberg integral on GSp2 forsquare-free levels

Key Points

• The aim is to compute the Rankin-Selberg integral for vector-valued Siegel cusp forms at square-free levels.
• Explicit evaluation of the Rankin-Selberg type integral for square-free levels.
• Analysis of local zeta integrals with specific test functions in Bessel models.
• Evaluation of irreducible admissible representations.
• Exact evaluations of local zeta integrals were obtained for chosen test functions.
• The computations provide insights into the relationships between the zeta integrals and Siegel cusp forms.
• The findings enhance understanding of number theory related to the Rankin-Selberg framework.