PreprintCC0arXiv
Unconditional Bounds for Two, Three and Four Consecutive Moderate Gaps between Zeros of the Riemann Zeta Function
Abstract
We prove unconditional positive-proportion results for consecutive moderate gaps between zeros of the Riemann zeta function. More precisely, for every fixed 0<c≤ 1/4, the lower asymptotic densities, normalized by N(T), of the occurrences of two, three, and four consecutive gaps, each of length at least 2πc/log T, are at least 0.3450014…, 0.1812517…, and 0.0175021…, respectively. Here, zeros are ordered by ordinate and counted with multiplicity, and N(T) denotes the number of nontrivial zeros with ordinates in (0,T]. These bounds address the corresponding cases of a question of Gonek and Sahay. The proof combines the methods of Alpöge--Furman and Lamzouri with local spectral estimates and cluster counting.
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BibTeX
@misc{angon2026unconditional,
title = {{Unconditional Bounds for Two, Three and Four Consecutive Moderate Gaps between Zeros of the Riemann Zeta Function}},
author = {César Angón and Erick Ross and Ze Sen Tang and Boyang Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22927},
eprint = {2610.22927},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22927},
note = {CC0},
}
RIS
TY - UNPB
TI - Unconditional Bounds for Two, Three and Four Consecutive Moderate Gaps between Zeros of the Riemann Zeta Function
AU - César Angón
AU - Erick Ross
AU - Ze Sen Tang
AU - Boyang Zhao
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.22927
UR - https://arxiv.org/abs/2610.22927
AB - We prove unconditional positive-proportion results for consecutive moderate gaps between zeros of the Riemann zeta function. More precisely, for every fixed 0<c≤ 1/4, the lower asymptotic densities, normalized by N(T), of the occurrences of two, three, and four consecutive gaps, each of length at least 2πc/log T, are at least 0.3450014…, 0.1812517…, and 0.0175021…, respectively. Here, zeros are ordered by ordinate and counted with multiplicity, and N(T) denotes the number of nontrivial zeros with ordinates in (0,T]. These bounds address the corresponding cases of a question of Gonek and Sahay. The proof combines the methods of Alpöge--Furman and Lamzouri with local spectral estimates and cluster counting.
ER -