Testing the functional equation of a high-degree Euler product

Abstract

WestudytheL-functionsassociatedtoSiegelmodularforms—equivalently, automorphic representations of GSp.4;AQ/—both theoretically and numerically. For the L-functions of degrees 10, 14, and 16 we perform representation theoretic calculations to cast the Langlands L-function in classical terms. We develop a precise notion of what it means to test a conjectured functional equation for an L-function, and we apply this to the degree-10 adjoint L-function associated to a Siegel modular form.