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 L-functions. In the case of the Riemann zeta function, their conjecture states that the 2k-th absolute moment of zeta on the critical line is asymptotically given by a certain 2k-fold residue integral. This residue integral can be expressed as a polynomial of degree k2, whose coefficients are given in exact form by elaborate and complicated formulas. In this article, uniform asymptotics for roughly the first k 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.