4 research outputs found
Lower order terms for the moments of symplectic and orthogonal families of -functions
We derive formulas for the terms in the conjectured asymptotic expansions of
the moments, at the central point, of quadratic Dirichlet -functions,
, and also of the -functions associated to quadratic twists
of an elliptic curve over \Q. In so doing, we are led to study determinants
of binomial coefficients of the form .Comment: 34 pages, 4 table
Uniform asymptotics for the full moment conjecture of the Riemann zeta function
Conrey, Farmer, Keating, Rubinstein, and Snaith, recently conjectured
formulas for the full asymptotics of the moments of -functions. In the case
of the Riemann zeta function, their conjecture states that the -th absolute
moment of zeta on the critical line is asymptotically given by a certain
-fold residue integral. This residue integral can be expressed as a
polynomial of degree , whose coefficients are given in exact form by
elaborate and complicated formulas. In this article, uniform asymptotics for
roughly the first coefficients of the moment polynomial are derived.
Numerical data to support our asymptotic formula are presented. An application
to bounding the maximal size of the zeta function is considered.Comment: 53 pages, 1 figure, 2 table