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May 24, 2026Open Access

p -adic L -functions for GSp ( 4 ) × GL ( 2 ) , II

Key Points

This research aims to construct a four-variable p-adic L-function for cuspidal Hida families on GSp(4) × GL(2).
Constructed a p-adic L-function for cuspidal Hida families on GSp(4) × GL(2).
Computed Archimedean zeta integrals using a partial interpolation formula and Yoshida lifts.
Utilized previously established p-adic L-functions for analysis.
Proved a complete interpolation formula for the constructed p-adic L-function.
Demonstrated the computation of Archimedean zeta integrals through novel methodologies.

Abstract

We construct a four-variable p -adic L -function for cuspidal Hida families on GSp ( 4 ) × GL ( 2 ) and prove a complete interpolation formula for it. The Archimedean zeta integrals are computed by using a partial interpolation formula for the four-variable p -adic L -function, combined with Yoshida lifts and some previously constructed p -adic L -functions—specifically Kubota–Leopoldt p -adic L -functions, Rankin–Selberg p -adic L -functions, and p -adic (standard) L -functions for Sp ( 4 ) .

p -adic L -functions for GSp ( 4 ) × GL ( 2 ) , II

Key Points

Abstract

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