Conjectures and Experiments Concerning the Moments of L(1/2, χ d )

We report on some extensive computations and experiments concerning the moments of quadratic Dirichlet L-functions at the critical point. We computed the values of L(1/2, χ d ) for −5×1010<d<1.3×1010 in order to numerically test conjectures concerning the moments ∑|d|<X L(1/2, χ d ) k . Specifically, we tested the full asymptotics for the moments conjectured by Conrey, Farmer, Keating, Rubinstein, and Snaith, as well as the conjectures of Diaconu, Goldfeld, Hoffstein, and Zhang concerning additional lower-order terms in the moments. We also describe the algorithms used for this large-scale computation.

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