On a level analog of Selberg's result on $S(t)$
Abstract
Let $S(t,f)=\pi^{-1}\arg L(1/2+it, f)$, where $f$ is a holomorphic Hecke cusp form of weight $2$ and prime level $q$. In this paper, we establish an asymptotic formula for the moments of $S(t,f)$ without assuming the GRH.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.14867
- arXiv:
- arXiv:2407.14867
- Bibcode:
- 2024arXiv240714867S
- Keywords:
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- Mathematics - Number Theory
- E-Print:
- 19 pages