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The Rankin–Selberg
integral on $\mathrm{GSp}_2$ for square-free levels
Seiji Kuga and Masao Tsuzuki |
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Vol. 342 (2026), No. 2, 299–350
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Abstract |
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We explicitly compute the Rankin–Selberg type integral introduced by Piatetski-Shapiro over adeles for vector-valued Siegel cusp forms of square-free levels . On the way, for particular test functions in the Bessel models of irreducible admissible representations, exact evaluations of the local zeta integrals are given. |
Keywords
Siegel modular forms, Rankin–Selberg integral
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Mathematical Subject Classification
Primary: 11F46
Secondary: 11F67
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Milestones
Received: 21 July 2024
Revised: 22 November 2025
Accepted: 27 December 2025
Published: 23 April 2026
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Authors |
| Seiji Kuga | |
| Faculty of Science and
Technology Sophia University Tokyo Japan |
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| Masao Tsuzuki | |
| Faculty of Science and
Technology Sophia University Tokyo Japan |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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