Diophantine approximation with prime denominator in quadratic number fields under GRH

Fuente: arXiv
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Main Authors: Baier, Stephan, Das, Sourav, Molla, Esrafil Ali
Format: Preprint
Published: 2023
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author Baier, Stephan
Das, Sourav
Molla, Esrafil Ali
author_facet Baier, Stephan
Das, Sourav
Molla, Esrafil Ali
contents Matomäki proved that if $α\in \mathbb{R}$ is irrational, then there are infinitely many primes $p$ such that $|α-a/p|\le p^{-4/3+\varepsilon}$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2312_02628
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Diophantine approximation with prime denominator in quadratic number fields under GRH
Baier, Stephan
Das, Sourav
Molla, Esrafil Ali
Number Theory
11J71, 11R11, 11R42, 11R44
Matomäki proved that if $α\in \mathbb{R}$ is irrational, then there are infinitely many primes $p$ such that $|α-a/p|\le p^{-4/3+\varepsilon}$ 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.
title Diophantine approximation with prime denominator in quadratic number fields under GRH
topic Number Theory
11J71, 11R11, 11R42, 11R44
url https://arxiv.org/abs/2312.02628