# Asymptotic mean square of product of higher derivatives of the zeta-function and Dirichlet polynomials

Speaker: Mithun Das

Date: Tue, Jul 26, 2022

Conference: Moments of L-functions Workshop

Subject:

Class: Scientific

### Abstract:

We discuss the asymptotic behavior of the mean square of higher derivatives of the Riemann zeta function or Hardy's $Z$-function product with a Dirichlet polynomial in a short interval. As an application, we obtain a refinement of some results by Levinson--Montgomery as well as Ki--Lee on zero density estimates of higher derivatives of the Riemann zeta function near the critical line. Also, we obtain a zero distribution result for Matsumoto--Tanigawa's $\eta_k$-function. This is joint work with S. Pujahari.