Moments of real Dirichlet $L$-functions and multiple Dirichlet series
Moments of real Dirichlet $L$-functions and multiple Dirichlet series
We consider the multiple Dirichlet series associated to the $k$th moment of real Dirichlet $L$-functions, and prove that it has a meromorphic continuation to a specific region in $\mathbb{C}^{k+1}$, which is conditional under the generalized Lindel\"of hypothesis for $k\geq 5$. As a corollary, we obtain asymptotic formulas for the first …