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PreprintarXiv licencearXiv

Half-sized gaps between zeros of the Riemann zeta function

  • Andriy Bondarenko
  • Winston Heap
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Abstract

Assuming the Riemann hypothesis, we prove that the lower limit of the normalised gaps between consecutive zeros of the Riemann zeta function is at most 1/2. Our methods utilise a more efficient method for detecting gaps with short Dirichlet polynomials. Specifically, we apply resonance to a quotient of shifted zeta functions, rather than to the number of zeros in a short interval, using a Möbius resonator adapted to the symmetry between the shifts.

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Cite

BibTeXRIS
BibTeX
@misc{bondarenko2026halfsized,
  title = {{Half-sized gaps between zeros of the Riemann zeta function}},
  author = {Andriy Bondarenko and Winston Heap},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26038},
  eprint = {2610.26038},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26038},
}
RIS
TY  - UNPB
TI  - Half-sized gaps between zeros of the Riemann zeta function
AU  - Andriy Bondarenko
AU  - Winston Heap
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26038
UR  - https://arxiv.org/abs/2610.26038
AB  - Assuming the Riemann hypothesis, we prove that the lower limit of the normalised gaps between consecutive zeros of the Riemann zeta function is at most 1/2. Our methods utilise a more efficient method for detecting gaps with short Dirichlet polynomials. Specifically, we apply resonance to a quotient of shifted zeta functions, rather than to the number of zeros in a short interval, using a Möbius resonator adapted to the symmetry between the shifts.
ER  -