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

In our earlier paper, based on a paper by Bump and Ginzburg, we used an Eisenstein series on the double cover of to obtain an integral representation of the twisted symmetric square L-function of . Using that, we showed that the (incomplete) twisted symmetric square L-function of is holomorphic for . 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 and .