Multivariate Rankin–Selberg Integrals on GL4 and GU(2, 2)

Abstract

AbstractInspired by a construction by Bump, Friedberg, and Ginzburg of a two-variable integral representation on GSp4 for the product of the standard and spin L-functions, we give two similar multivariate integral representations. The first is a three-variable Rankin–Selberg integral for cusp forms on PGL4 representing the product of the L-functions attached to the three fundamental representations of the Langlands L-group SL4(C). The second integral, which is closely related, is a two-variable Rankin–Selberg integral for cusp forms on PGU(2, 2) representing the product of the degree 8 standard L-function and the degree 8 exterior square L-function.