Moments of higher derivatives related to Dirichlet L-functions

Abstract: The distribution of values of Dirichlet $L$-functions $L(s, \chi)$ for variable $\chi$ has been studied extensively and has a vast literature. Moments of higher derivatives has been studied as well, by Soundarajan, Sono, Heath-Brown etc. However, the study of the same for the logarithmic derivative $L’(s, \chi)/ L(s, \chi)$ is much more recent and was initiated by Ihara, Murty etc. In this talk we will discuss higher derivatives of the logarithmic derivative and present some new results related to their distribution and moments at $s=1$.

combinatoricsnumber theory

Audience: researchers in the topic

Lethbridge number theory and combinatorics seminar