Conditional estimates for the logarithmic derivative of Dirichlet L-functions

Chirre A.; Hagen M.V.; Simonič A. · Indagationes Mathematicae (2024) · DOI: 10.1016/j.indag.2023.07.005

Resumen

Assuming the Generalized Riemann Hypothesis, we establish explicit bounds in the q-aspect for the logarithmic derivative L′/Lσ,χ of Dirichlet L-functions, where χ is a primitive character modulo q≥1030 and 1/2+1/loglogq≤σ≤1−1/loglogq. In addition, for σ=1 we improve upon the result by Ihara, Murty and Shimura (2009). Similar results for the logarithmic derivative of the Riemann zeta-function are given.

Instituciones: Pontificia Universidad Católica del Perú