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

Citation

Saha, Abhishek (2009) On Critical Values of L-Functions for Holomorphic Forms on GSp(4) X GL(2). Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5HWD-TH76. https://resolver.caltech.edu/CaltechETD:etd-05222009-162600

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.

Thesis Files