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- W3207108972 abstract "In this paper we prove a conjecture of Ginzburg and Soudry on an integral representation for the $L$-function $L^S(s, pitimes tau)$ attached to a pair $(pi, tau)$ of irreducible automorphic cuspidal representations of $mathrm{Sp}_4({mathbb A})$ and $mathrm{GL}_2({mathbb A})$, which is derived from the generalized doubling method of Cai, Friedberg, Ginzburg and Kaplan. We show that the integral unfolds to a non-unique model and analyze it using the New Way method of Piatetski-Shapiro and Rallis. As applications, we determine the poles of $L^S(s, pitimes tau)$ and relate the existence of the poles to the non-vanishing of certain period integrals. Moreover, for certain family of cuspidal representations $tau$ of $mathrm{GL}_2({mathbb A})$, we prove that $L^S(s, pitimes tau)$ is holomorphic." @default.
- W3207108972 created "2021-10-25" @default.
- W3207108972 creator A5091437311 @default.
- W3207108972 date "2021-10-11" @default.
- W3207108972 modified "2023-09-23" @default.
- W3207108972 title "$L$-function for $mathrm{Sp}(4)timesmathrm{GL}(2)$ via a non-unique model" @default.
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- W3207108972 doi "https://doi.org/10.48550/arxiv.2110.05693" @default.
- W3207108972 hasPublicationYear "2021" @default.
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