Pullbacks of Eisenstein series from GU(3,3) and critical L-values for GSp(4) X GL(2)
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.
Keywords
Cite
@article{arxiv.0904.4005,
title = {Pullbacks of Eisenstein series from GU(3,3) and critical L-values for GSp(4) X GL(2)},
author = {Abhishek Saha},
journal= {arXiv preprint arXiv:0904.4005},
year = {2009}
}
Comments
45 pages; Some notational changes made, inaccuracies eliminated and typos fixed in accordance with an anonymous referee's helpful comments. To appear in the Pacific Journal of Mathematics