Moment Polynomials for the Riemann Zeta Function

Abstract

In this thesis we calculated the coefficients of moment polynomials of the Riemann zeta function for k= 4, 5, 6...13 using cubic acceleration, which is an improved method from quadratic acceleration. We then numerically verified the moment conjectures. The results we obtained appear to support the conjectures. We also present a brief history of the moment polynomials by illustrating some of the important results of the field along with proofs for two of the classic results. The heuristics to find the integral moments of the Riemann zeta function is described in this thesis as well.