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arXiv · 2610.28527

Small and large gaps between zeros of Dirichlet $L$-functions

Benjamin Durkan·Andrew Pearce-Crump
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Abstract

For every fixed primitive Dirichlet $L$-function and every $\varepsilon>0$, we prove unconditionally that infinitely many consecutive zeros have spacing less than $1/2+\varepsilon$ times the mean. Assuming the Riemann Hypothesis, we also prove a positive proportion of such spacings for the Riemann zeta-function, and infinitely many spacings greater than $3.63$ times the mean for every fixed primitive Dirichlet $L$-function.

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BibTeXRIS

Benjamin Durkan, Andrew Pearce-Crump. 2026-10-20. Small and large gaps between zeros of Dirichlet $L$-functions. https://arxiv.org/abs/2610.28527

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