Alexandre Lartaux, IMJ-PRG

May 14th, 2021 12:00-12:30 pm CEST

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

Abstract : Let $K$ be a cyclic extension of 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($K$/ℚ), which is

r$$₃($n$)$=$(1*χ * χ$2$ )($n$).

In this talk, we investigate an asymptotic estimate for 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.