The negative Pell equation and applications

Abstract: In this talk we will study the negative Pell equation, which is the conic $C_D : x^2 - D y^2 = -1$ to be solved in integers $x, y \in \mathbb{Z}$. We shall be concerned with the following question: as we vary over squarefree integers $D$, how often is $C_D$ soluble? Stevenhagen conjectured an asymptotic formula for such $D$. Fouvry and Klüners gave upper and lower bounds of the correct order of magnitude. We will discuss a proof of Stevenhagen's conjecture, and potential applications of the new proof techniques. This is joint work with Carlo Pagano.

number theory

Audience: researchers in the topic

Harvard number theory seminar