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October 8, 2025Open Access

The positivity technique and low-lying zeros of Dirichlet L-functions

Key Points

Sharpened results on the distribution of low-lying zeros of dirichlet l-functions were rediscovered.
The positivity technique provides a rigorous approach to analyze low-lying zeros of dirichlet l-functions.
Estimates were effectively conditional on the validity of the generalized riemann hypothesis.
Results were generalized to a wider class of l-functions, indicating broader applications.

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 L-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 L-functions and provide effective conditional estimates for the lowest zeros of Dirichlet L-functions.

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Cite This Study

Tiebin Zhao (Thu,) studied this question.

synapsesocial.com/papers/68e62de1a8c0c6d458740173 https://doi.org/https://doi.org/10.48550/arxiv.2503.15832

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