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June, 2022 Moments of $S(t,f)$ Associated with Holomorphic Hecke Cusp Forms
Sheng-Chi Liu, Jemin Shim
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Taiwanese J. Math. 26(3): 463-482 (June, 2022). DOI: 10.11650/tjm/211207

Abstract

Let $S(t,f) := \pi^{-1} \arg L(1/2+it,f)$, where $f$ is a holomorphic Hecke cusp form for $\operatorname{SL}_2(\mathbb{Z})$ of weight $k$. We establish an asymptotic formula for the moments of $S(t,f)$.

Funding Statement

The first author was supported by a grant (#344139) from the Simons Foundation.

Acknowledgments

The authors would like to thank the referee for his/her careful reading and valuable comments.

Citation

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Sheng-Chi Liu. Jemin Shim. "Moments of $S(t,f)$ Associated with Holomorphic Hecke Cusp Forms." Taiwanese J. Math. 26 (3) 463 - 482, June, 2022. https://doi.org/10.11650/tjm/211207

Information

Received: 31 May 2021; Revised: 4 November 2021; Accepted: 15 December 2021; Published: June, 2022
First available in Project Euclid: 29 December 2021

Digital Object Identifier: 10.11650/tjm/211207

Subjects:
Primary: 11F66 , 11F72

Keywords: $S(t,f)$ functions , holomorphic modular forms

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

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Vol.26 • No. 3 • June, 2022
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