The first moment of primitive cubic L-functions with fixed genus

2:00pm, Wednesday 23rd Sep 2026

Abstract

We investigate the mean value of the first moment of primitive cubic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Employing a double Dirichlet series approach, we establish an error term of size $q^{(7/8+\epsilon)g}$. Our method significantly reduces computational complexity by avoiding the computation of the residue.