First moment of quadratic Dirichlet $L$-functions with secondary terms

Abstract

We study the first moment of primitive quadratic Dirichlet $L$-functions. Assuming the Riemann hypothesis and the generalized Lindelöf hypothesis, we obtain an asymptotic formula at the central point with error $O(X^{1/4+\epsilon })$, and identify lower-order terms of size $X^{1/3}\log X$.

arXiv commentCorrected title and other minor fixes; 34 pages