Diophantine approximation with prime denominator in quadratic number fields under GRH

Stephan Baier; Sourav Das; Esrafil Ali Molla

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arXiv · 2312.02628

Diophantine approximation with prime denominator in quadratic number fields under GRH

Stephan Baier·Sourav Das·Esrafil Ali Molla

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Abstract

Matom\"aki proved that if $\alpha\in \mathbb{R}$ is irrational, then there are infinitely many primes $p$ such that $|\alpha-a/p|\le p^{-4/3+\varepsilon}$ for a suitable integer a. In this paper, we extend this result to all quadratic number fields under the condition that the Grand Riemann Hypothesis holds for their Hecke $L$-functions.

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Stephan Baier, Sourav Das, Esrafil Ali Molla. 2023-12-05. Diophantine approximation with prime denominator in quadratic number fields under GRH. https://arxiv.org/abs/2312.02628

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