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September 27, 2025Open Access

Conditional estimates on the argument of Dirichlet L-functions with applications to low-lying zeros

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Conditional estimates show bounds on the mean square of Dirichlet L-function arguments, revealing insights into their distribution.
Under the generalized Riemann hypothesis, a new lower bound is established for the proportion of Dirichlet L-functions with low-lying zeros.
The results highlight that a positive proportion of Dirichlet L-functions have their first zero located significantly close to the central point.
Alternative proofs provided for existing results on low-lying zeros enhance the understanding of Dirichlet L-function behavior.

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Analysis under the generalized Riemann hypothesis reveals bounds on Dirichlet L-function arguments, indicating implications for low-lying zeros.

Tiebin Zhao (2025) studied this question.

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Analysis under the generalized Riemann hypothesis reveals bounds on Dirichlet L-function arguments, indicating implications for low-lying zeros.