Integral points on quadratic equations

Abstract: Fix a prime number $l \equiv 3 \bmod 4$. In this talk we study how often the equation $x^2 - dy^2 = l$ is soluble in integers x and y as we vary $d$ over squarefree integers divisible by our fixed prime $l$. We will discuss how this question can be rephrased in terms of the 2-part of the narrow class group of $\mathbb{Q}(\sqrt{d})$. Then we sketch how one can use the recent ideas of Alexander Smith to obtain the distribution of these class groups. This is joint work with Carlo Pagano.

algebraic geometrynumber theory

Audience: researchers in the topic

MAGIC (Michigan - Arithmetic Geometry Initiative - Columbia)

Series comments: Description: Research seminar in arithmetic geometry

(Zoom password = order of the alternating group on six letters)