Year: 2026
Type: article
Abstract: In this paper, we show that for each sufficiently large integer upper H H $H$ , there is a real cubic number alpha α $\alpha$ and a rational number r r $r$ , both of height smaller than upper H H $H$ , such that 0 less than alpha minus r less than 272 divided by upper H Superscript 4 0 < α − r < 272 / H 4 $0\lt \alpha -r\lt 272/H^4$ . The exponent 4 4 $4$ of upper H H $H$ in this inequality is best possible. The numbers alpha α $\alpha$ and r r $r$ are both constructed explicitly. We also show that a necessary and suf
Source: Glasgow Mathematical Journal
Author: Artūras Dubickas
Institution: Vilnius University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7165019361