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

Martin Čech

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arXiv · 2509.03197

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

Martin Čech

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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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Martin Čech. 2025-09-03. First moment of quadratic Dirichlet $L$-functions with secondary terms. https://arxiv.org/abs/2509.03197

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