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The fourth moment of quadratic Dirichlet L-functions

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Abstract

We study the fourth moment of quadratic Dirichlet L-functions at \(s= \frac{1}{2}\). We show an asymptotic formula under the generalized Riemann hypothesis, and obtain a precise lower bound unconditionally. The proofs of these results follow closely arguments of Soundararajan and Young (J Eur Math Soc 12(5):1097–1116, 2010) and Soundararajan (Ann Math (2) 152(2):447–488, 2000).

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Acknowledgements

I would like to thank my supervisors Habiba Kadiri and Nathan Ng, for suggesting this problem to me, and for having numerous helpful discussions. I would also like to thank Matilde Lalín, Keiju Sono and Peng-jie Wong for their valuable comments. Lastly, I would like to thank the referee for their extensive feedback and constructive comments.

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  1. Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, AB, T1K 3M4, Canada

    Quanli Shen

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  1. Quanli Shen
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Correspondence to Quanli Shen.

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Shen, Q. The fourth moment of quadratic Dirichlet L-functions. Math. Z. 298, 713–745 (2021). https://doi.org/10.1007/s00209-020-02609-2

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