Peter Koymans

## Institution:

Univ. of Michigan

## Time:

Thursday, April 21, 2022 - 10:00am to 11:00am

## Location:

https://uci.zoom.us/j/95268809663

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 Kluners 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.