PreprintCC BY 4.0arXiv
Diophantine approximation by primes and Landau--Siegel zeros
Abstract
Let α>0 be an irrational number of finite type and let β∈ℝ. Assuming the infinitude of Siegel zeros (respectively, sufficiently strong Siegel zeros), we show that for every sufficiently small ε>0, there exist infinitely many primes p such that |αp+β|≤ p−1/3+ε (respectively, |αp+β|≤ p−1/3−1/20).
Related
BibTeX
@misc{leung2026diophantine,
title = {{Diophantine approximation by primes and Landau--Siegel zeros}},
author = {Sun-Kai Leung and Stelios Sachpazis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30207},
eprint = {2609.30207},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30207},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Diophantine approximation by primes and Landau--Siegel zeros
AU - Sun-Kai Leung
AU - Stelios Sachpazis
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30207
UR - https://arxiv.org/abs/2609.30207
AB - Let α>0 be an irrational number of finite type and let β∈ℝ. Assuming the infinitude of Siegel zeros (respectively, sufficiently strong Siegel zeros), we show that for every sufficiently small ε>0, there exist infinitely many primes p such that |αp+β|≤ p^−1/3+ε (respectively, |αp+β|≤ p^−1/3−1/20).
ER -