A Mean Value Theorem for the Diophantine Equation $axy-x-y=n$

Abstract

In this paper, we prove an asymptotic formula for the average number of solutions to the Diophantine equation $axy-x-y=n$ in which $a$ is fixed and and $n$ varies.

arXiv comment11 pages, to appear in Acta Math. Hungar. A couple of typos are corrected in the new version