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arXiv · 2610.26038

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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Andriy Bondarenko, Winston Heap. 2026-10-19. Half-sized gaps between zeros of the Riemann zeta function. https://arxiv.org/abs/2610.26038

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