The negative Pell equation

Abstract

By applying methods recently developed by A. Smith with regards to Goldfeld's conjecture, we show that the density of square-free integers $d$ in $[1,N]$ for which the negative Pell equation $x^2-d{y}^2=-1$ has a solution is as predicted by the model of Stevenhagen.

We made a mistake regarding applying A. Smith's methods, in particular eq. (9.8) in our paper is not valid