Moments of central values of quartic Dirichlet L-functions

Multiple Dirichlet Series and Moments of Zeta and L–functions

This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic continuation and polar divisors of certain such series imply, as a consequence, precise asymptotics (previously conjectured via random matrix theory) for moments o...

Second Moments of Dirichlet L-functions Weighted by Kloosterman Sums

Central Values of Degree Six L-functions

Let κ′, κ ≥ 3 be two odd integers. Let f (resp. g) be a normalized holomorphic modular form of weight 2κ (resp. κ′ + 1) and level one on the upper half plane h. Assume that they are Hecke eigenforms. Let L(s, Sym g×f) be the completed degree six L-function and we normalize so that s = 1 2 is the center of symmetry. Let 〈−,−〉 be the Petersson inner product, defined using the usual measure on h s...

Computing Central Values of L-functions

How fast can we compute the value of an L-function at the center of the critical strip? We will divide this question into two separate questions while also making it more precise. Fix an elliptic curve E defined over Q and let L(E, s) be its L-series. For each fundamental discriminant D let L(E,D, s) be the L-series of the twist ED of E by the corresponding quadratic character; note that L(E, 1...

On the Mean Values of Dirichlet L-functions

Abstract. We study the 2k-th power moment of Dirichlet L-functions L(s, χ) at the centre of the critical strip (s = 1/2), where the average is over all primitive characters χ (mod q). We extend to this case the hybrid Euler-Hadamard product results of Gonek, Hughes and Keating for the Riemann zeta-function. This allows us to recover conjectures for the moments based on random matrix models, inc...