First moment of quadratic Dirichlet $L$-functions with secondary terms
Martin Čech
公開日: 2025/9/3
Abstract
We study the first moment of primitive quadratic Dirichlet $L$-functions. Assuming the Riemann hypothesis and the generalized Lindel\"of hypothesis, we obtain an asymptotic formula at the central point with error $O(X^{1/4+\epsilon})$, and identify lower-order terms of size $X^{1/3}\log X$.