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This is a Quantitative Study study.

October 12, 2025Open Access

First moment of quadratic Dirichlet L-functions with secondary terms

Key Points

An asymptotic formula at the central point reveals crucial insights into quadratic dirichlet l-functions.
Under the Riemann hypothesis, the leading error term is shown to be O(X^{1/4+ε}), indicating considerable significance.
Lower-order terms identified include X^{1/3}log X, emphasizing their importance in the formula's accuracy.
The study follows a rigorous mathematical approach assuming the generalized Lindelöf hypothesis.

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+ε), and identify lower-order terms of size X^1/3 X.

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Cite This Study

Martin Čech (Wed,) studied this question.

synapsesocial.com/papers/68ec384042a190b2c3519829 https://doi.org/https://doi.org/10.48550/arxiv.2509.03197

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