On the number of ideals with norm a binary form of degree 3

Abstract: Let $K$ be a cyclic extension of $\mathbb Q$ of degree 3. If $r_3(n)$ denotes the number of ideals of $O_K$ of norm $n,$ we have a relation between the function $r_3$ and a non trivial Dirichlet character of $\Gal(K/\mathbb Q)$, which is $$r_3(n) = (1 ∗ \chi ∗ \chi^2)(n).$$ In this talk, we investigate an asymptotic estimate of the number of ideals of $O_K$ with norm is a binary form of degree 3, using this equality and a new result on Hooley's Delta function.

algebraic geometrycombinatoricsdynamical systemsgeneral topologynumber theory

Audience: researchers in the topic

ZORP (zoom on rational points)

Series comments: 2 talks on a Friday, roughly once per month.

Online coffee break in between.