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PreprintCC BY 4.0arXiv

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 ε>0, we prove unconditionally that infinitely many consecutive zeros have spacing less than 1/2+ε 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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Cite

BibTeXRIS
BibTeX
@misc{durkan2026small,
  title = {{Small and large gaps between zeros of Dirichlet $L$-functions}},
  author = {Benjamin Durkan and Andrew Pearce-Crump},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28527},
  eprint = {2610.28527},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28527},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Small and large gaps between zeros of Dirichlet L-functions
AU  - Benjamin Durkan
AU  - Andrew Pearce-Crump
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.28527
UR  - https://arxiv.org/abs/2610.28527
AB  - For every fixed primitive Dirichlet L-function and every ε>0, we prove unconditionally that infinitely many consecutive zeros have spacing less than 1/2+ε 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.
ER  -