Document Type
Lecture
Publication Date
11-9-2022
Abstract
I will review the history of value-distribution problems for the Riemann zeta function and other L-functions, and I survey some recent results on this topic. I will also discuss the methods used in studying the value-distribution of the logarithmic derivatives of a family of quadratic twist L-functions with the goal of describing an upper bound on the discrepancy in the convergence of this family to its limiting distribution. In particular, I discuss joint work with Amir Akbary in which we obtain discrepancy bounds for the family L'/L(1 + it, χ_D) of logarithmic derivatives of quadratic twists of a fixed automorphic L-function at a point on the edge of the critical strip. This result can be considered as an automorphic analogue of a recent result of Lamzouri, Lester, and Radziwill for the logarithm of the Riemann zeta function. We also give an application of our result related to the small values of |L'/L(1, χ_D)| as D varies over fundamental discriminants.
Relational Format
presentation
Recommended Citation
Hamieh, Alia, "Distribution of Values of Logarithmic Derivatives of L-Functions" (2022). Algebra/Number Theory Seminar. 12.
https://egrove.olemiss.edu/math_algebra_number_theory/12
