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

2026/07/01 by Tianyu Zhao
Mathematics · #Analytic Number Theory Research #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · doi:10.1016/j.jnt.2026.06.013

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.

Citations

• Hilbert spaces and low-lying zeros of L-functions
• Nonvanishing of Quadratic Dirichlet L-Functions at S = &#189
• On the Zeros of the Dirichlet L-Functions

Related

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• Detecting zeros of Dirichlet L-functions via the Riemann zeta-function
• Conditional estimates on the argument of Dirichlet L-functions with applications to low-lying zeros
• The Riemann Hypothesis for Dirichlet L Functions
• Low-lying zeros of quadratic Dirichlet L-functions: A transition in the Ratios Conjecture