Pullbacks of Eisenstein series from GU(3,3) and critical L-values for GSp(4) X GL(2)

2009/04/25 by Abhishek Saha, Saha, Abhishek
Mathematics · #11F46 #11F67 #11F70 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0904.4005

openalex publication_date 2009/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a genus two Siegel newform and g a classical newform, both of squarefree levels and of equal weight l. We prove a pullback formula for certain Eisenstein series -- thus generalizing a construction of Shimura -- and use this to derive an explicit integral representation for the degree eight L-function L(s, F X g). This integral representation involves the pullback of a simple Siegel-type Eisenstein series on the unitary group GU(3,3). As an application, we prove a reciprocity law -- predicted by Deligne's conjecture -- for the critical special values L(m, F X g) where m is an integer, 2 <= m <= l/2-1.

Citations

• Bessel models for lowest weight representations of GSp(4,R)

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