H. Jung

The first moment of quadratic Dirichlet $L$-functions in the even hyperelliptic ensemble

We establish an asymptotic formula for the first moment of the central values of quadratic Dirichlet $L$-functions in the even hyperelliptic ensemble $\mathcal{H}_{2g+2}$ over $\mathbb{F}_q[x]$, for every fixed odd prime power $q$. Working with the completed $L$-function yields an exact two-term central-value formula w...