Moments of the Dedekind zeta function and other non-primitive L-functions

Abstract

We give a conjecture for the moments of the Dedekind zeta function of a Galois extension via the hybrid product method. The moments of the product of primes are evaluated using the Montgomery-Vaughan mean value theorem whilst for the moments of the product over zeros we give a heuristic argument involving random matrix theory. The asymptotic for the first moment of the product over zeros is then proved for quadratic extensions. We are also able to reproduce our main conjecture in the quadratic case by using a modified version of the moments recipe. Finally, we generalise our methods to give a conjecture for moments of non-primitive L-functions.