Year: 2026
Type: preprint
Abstract: Let $α>0$ be an irrational number of finite type and let $β\in\mathbb{R}$. Assuming the infinitude of Siegel zeros (respectively, sufficiently strong Siegel zeros), we show that for every sufficiently small $\varepsilon>0$, there exist infinitely many primes $p$ such that \begin{gather*} \|αp+β\|\leq p^{-1/3+\varepsilon} \qquad\text{(respectively, }\|αp+β\|\leq p^{-1/3-1/20}\text{)}. \end{gather*}
Source: arXiv (Cornell University)
Authors: Leung, Sun-Kai, Sachpazis, Stelios
Institutions: Charles University, University of Oxford
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Univerzita Karlova v Praze
Award: G284571301
OpenAlex ID: W7214326821