香蕉视频

Title:聽Mean Values of Long Dirichlet Polynomials with Higher Divisor Coefficients.

Abstract:聽The 2k-th moments and shifted moments of the Riemann zeta function can be modelled by mean values of Dirichlet polynomials with higher divisor coefficients. In this talk, I discuss joint work with Nathan Ng where we establish an asymptotic formula for mean values of long Dirichlet polynomials with higher order shifted divisor functions as coefficients, assuming a conjectural formula for a certain family of additive divisor sums. This proves a conjecture of Coney-Keating (2015) under the assumption of an additive divisor conjecture. In an ongoing work, we use this result to establish a special case of a conjecture of Conrey-Gonek (1998) when the additive divisor conjecture is known.