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First moment of quadratic Dirichlet $L$-functions with secondary terms (2509.03197v1)
Published 3 Sep 2025 in math.NT
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 $X{1/3}\log X$.
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