Non-vanishing of Class Group L-functions for Number Fields with a Small Regulator

Ilya Khayutin

Let $E/\mathbb{Q}$ be a number field of degree $n$. We show that if $\mathrm{Reg}(E){\ll }_n|\mathrm{Disc}(E){|}^{1/4}$ then the fraction of class group characters for whic…