2008/08/11 by Ameya Pitale, Pitale, Ameya, Ralf Schmidt +1 · 1 citation
Mathematics · #11F67 (Secondary) #11F70 (Primary) 11F46 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F46 #msc:11F67 #msc:11F70
paper · pdf · doi:10.48550/arxiv.0808.1438
arxiv created 2008/08/11 · openalex publication_date 2008/08/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Furusawa has given an integral representation for the degree 8 L-function of GSp(4) x GL(2) and has carried out the unramified calculation. The local p-adic zeta integrals were calculated in our earlier work under the assumption that the GSp(4) representation πis unramified and the GL(2) representation τhas conductor p. In the present work we generalize to the case where the GL(2) 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) x GL(2) global L-function coming from classical holomorphic cusp forms with arbitrarily high level for the elliptic modular form.