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arXiv · 2511.13898

Upper bounds on gaps between zeros of $L$-functions

Tianyu Zhao
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Abstract

We prove two unconditional upper bounds on the gaps between ordinates of consecutive non-trivial zeros of a general $L$-function $L(s)$. This extends previous work of Hall and Hayman (2000) on the Riemann zeta-function and work of Siegel (1945) on Dirichlet $L$-functions. Interestingly, we observe that while Hall and Hayman's method gives a sharper estimate when the degree of $L(s)$ is sufficiently small compared to the analytic conductor, Siegel's method does better in the other regime.

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Tianyu Zhao. 2025-11-17. Upper bounds on gaps between zeros of $L$-functions. https://arxiv.org/abs/2511.13898

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