2015/05/05 by Joseph Hundley, Xin Shen, Hundley, Joseph +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.1505.01045
We consider a new integral representation for L(s1, Π× τ1) L(s2, Π× τ2), where Π is a globally generic cuspidal representation of GSp4, and τ1 and τ2 are two cuspidal representations of GL2 having the same central character. As and application, we find a new period condition for two such L functions to have a pole simultaneously. This points to an intriguing connection between a Fourier coefficient of a residual representation on GSO(12) and a theta function on \widetildeSp(16). A similar integral on GSO(18) fails to unfold completely, but in a way that provides further evidence of a connection.