GRH 条件下二次数域质分母的 Diophantine 近似算法

The Ramanujan Journal Pub Date : 2024-09-02 DOI:10.1007/s11139-024-00942-2

Stephan Baier, Sourav Das, Esrafil Ali Molla

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引用次数: 0

摘要

Matomäki 证明了如果 \(\alpha \in {\mathbb {R}}\) 是无理数，那么对于一个合适的整数 a，有无限多的素数 p 使得 \(|\alpha -a/p|\le p^{-4/3+\varepsilon }\) 存在。

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Diophantine approximation with prime denominator in quadratic number fields under GRH

Matomäki 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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The Ramanujan Journal

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