On a certain metaplectic Eisenstein series and the twisted symmetric square L-function

2015/06/15 by Takeda, Shuichiro · 1 citation
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1506.04791

Abstract

In our earlier paper, based on a paper by Bump and Ginzburg, we used an Eisenstein series on the double cover of GL(r) to obtain an integral representation of the twisted symmetric square L-function of GL(r). Using that, we showed that the (incomplete) twisted symmetric square L-function of GL(r) is holomorphic for Re(s) > 1. In this paper, we will determine the possible poles of this Eisenstein series more precisely and show that the (incomplete) twisted symmetric square L-function is entire except possible simple poles at s = 0 and s = 1.

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