Year: 2025
Type: preprint
Abstract: In the present paper we give very simple general statements which deal with approximation of a real number by rationals and are related to isolation phenomenon. In particular we study functions $ f(x)>f_1(x)>0$ such that existence of solutions $\frac{p}{q}$ of Diophantine inequality $ \left| α-\frac{p}{q}\right|< \frac{f(q)}{q^2} $ leads to the existence of solutions of inequality $ \left| α-\frac{p}{q}\right|< \frac{f_1(q)}{q^2} $.
Source: arXiv (Cornell University)
Authors: Pitcyn, Sergei, Moshchevitin, Nikolay
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7084626422
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