Moments of higher derivatives related to Dirichlet L-functions
Speaker: Samprit Ghosh
Date: Wed, Feb 7, 2024
Location: PIMS, University of Lethbridge, Zoom, Online
Conference: Lethbridge Number Theory and Combinatorics Seminar
Subject: Mathematics, Number Theory
Class: Scientific
Date: Wed, Feb 7, 2024
Location: PIMS, University of Lethbridge, Zoom, Online
Conference: Lethbridge Number Theory and Combinatorics Seminar
Subject: Mathematics, Number Theory
Class: Scientific
Abstract:
The distribution of values of Dirichlet L-functions \(L(s, \chi)\) for variable \(χ\) 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.
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