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April 26, 2026Pacific Journal of Mathematics0 citationsOpen Access

The Rankin–Selberg integral on GSp2 forsquare-free levels

SKSeiji KugaMTMasao Tsuzuki

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.

Abstract

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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Cite This Study

Kuga et al. (2026) studied this question.

synapsesocial.com/papers/69edabb84a46254e215b38d0https://doi.org/10.2140/pjm.2026.342.299
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