Zi-Wei Hong

A secondary term in the first moment of cubic $L$-functions over function fields

Let $q$ be a fixed odd prime power with $q\equiv2\pmod3$. We study the first moment of primitive cubic Dirichlet $L$-functions over $\Fq(T)$, ordered by their genus. By averaging the rational sieve variable in the double Dirichlet series of Hong and Fang, we obtain meromorphic continuation beyond the secondary polar di...