Stelios Sachpazis

Diophantine approximation by primes and Landau--Siegel zeros

Let $\alpha>0$ be an irrational number of finite type and let $\beta\in\mathbb{R}$. 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*} \|\alpha p+\beta\|\leq...