On Critical Values of L-Functions for Holomorphic Forms on GSp(4) X GL(2)

Author: Saha, Abhishek

Year: 2009

Degree: Dissertation (Ph.D.)

Advisor: Ramakrishnan, Dinakar

Committee Members: Ramakrishnan, Dinakar; Balasubramaniam, Baskar; Mantovan, Elena; Flach, Matthias

Option: Mathematics

DOI: 10.7907/5HWD-TH76

Abstract

Let F be a genus two Siegel newform and g a classical newform, both of squarefree levels and of equal weight ℓ. We derive an explicit integral representation for the degree eight L-function L(s, F x g). 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 ∈ Z, 2 ≤ m ≤ ℓ/2 -1. The proof of our integral representation has two major components: the generalization of an earlier integral representation due to Furusawa and a ``pullback formula" relating the complicated Eisenstein series of Furusawa with a simpler one on a higher rank group. The critical value result follows from our integral representation using rationality results of Garrett and Harris and the theory of nearly holomorphic forms due to Shimura.

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