Transfer of Siegel cusp forms of degree 2

2011/06/28 by Ameya Pitale, Abhishek Saha, Pitale, Ameya +3
Mathematics · #11F46 #11F67 #11F70 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1106.5611

openalex publication_date 2011/06/28 · openalex created_date 2022/05/12 · openalex updated_date 2026/07/28

Abstract

Let π be the automorphic representation of \GSp₄(\A) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and τ be an arbitrary cuspidal, automorphic representation of \GL₂(\A). Using Furusawa's integral representation for \GSp₄×\GL₂ combined with a pullback formula involving the unitary group \GU(3,3), we prove that the L-functions L(s,π×τ) are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations π have a functorial lifting to a cuspidal representation of \GL₄(\A). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of π to a cuspidal representation of \GL₅(\A). As an application, we obtain analytic properties of various L-functions related to full level Siegel cusp forms. We also obtain special value results for \GSp₄×\GL₁ and \GSp₄×\GL₂.

Citations

• On Euler Products and the Classification of Automorphic Representations I
• On the Saito-Kurokawa lifting
• On Certain L-Functions
• On the poles of AndrianovL-functions
• Bessel models for lowest weight representations of GSp(4,R)
• A relation between multiplicity one and Bocherer's conjecture

Related

• Integral Representaion for L-functions for GSp(4)xGL(2)
• Integral representation for L-functions for GSp(4) x GL(2), II
• Artin representations for GSp₄ attached to real analytic Siegel cusp forms of weight (2,1)
• A Cuspidality Criterion for the Exterior Square Transfer of Cusp Forms on GL(4)
• L-functions of S₃(\G₂(2,4,8))