L-functions for Gsp 4 × Gl 2 in the Case of High Gl 2 Conductor
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چکیده
Abstract. Furusawa [5] has given an integral representation for the degree 8 Lfunction of GSp 4 × GL2 and has carried out the unramified calculation. The local p-adic zeta integrals were calculated in the work [6] under the assumption that the GSp 4 representation π is unramified and the GL2 representation τ has conductor p. In the present work we generalize to the case where the GL2 representation has arbitrarily high conductor. The result is that the zeta integral represents the local Euler factor L(s, π × τ ) in all cases. As a global application we obtain a special value result for a GSp 4 × GL2 global L-function coming from classical holomorphic cusp forms with arbitrarily high level for the elliptic modular form.
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تاریخ انتشار 2008