On a Diophantine inequality with reciprocals

M. A. Korolev

Informatics and Automation, Analytic number theory, Tome 299 (2017), pp. 144-154.

Résumé

A sharpened lower bound is obtained for the number of solutions to an inequality of the form $\alpha \le \{(a\overline {n}+bn)/q\}\beta $, $1\le n\le N$, where $q$ is a sufficiently large prime number, $a$ and $b$ are integers with $(ab,q)=1$, $n\overline {n}\equiv 1 \pmod q$, and $0\le \alpha \beta \le 1$. The length $N$ of the range of the variable $n$ is of order $q^\varepsilon $, where $\varepsilon >0$ is an arbitrarily small fixed number.

Détail

Mots-clés : inverse residues
Keywords: fractional parts, Kloosterman sums.

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