The positivity technique and low-lying zeros of Dirichlet $L$-functions
Number Theory
2025-03-21 v1
Abstract
Assuming the generalized Riemann hypothesis, we rediscover and sharpen some of the best known results regarding the distribution of low-lying zeros of Dirichlet -functions. This builds upon earlier work of Omar, which relies on the classical positivity technique of explicit formulas. In addition, we generalize some of our results to a larger class of -functions and provide effective conditional estimates for the lowest zeros of Dirichlet -functions.
Keywords
Cite
@article{arxiv.2503.15832,
title = {The positivity technique and low-lying zeros of Dirichlet $L$-functions},
author = {Tianyu Zhao},
journal= {arXiv preprint arXiv:2503.15832},
year = {2025}
}