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arXiv · 2410.03473

On an unconditional spectral analog of Selberg's result on $S(t)$

Qingfeng Sun·Hui Wang
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Abstract

Let $S_j(t)=\frac{1}{\pi}\arg L(1/2+it, u_j)$, where $u_j$ is an even Hecke--Maass cusp form for $\rm SL_2(\mathbb{Z})$ with Laplacian eigenvalue $\lambda_j=\frac{1}{4}+t_j^2$. Without assuming the GRH, we establish an asymptotic formula for the moments of $S_j(t)$.

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Qingfeng Sun, Hui Wang. 2024-10-04. On an unconditional spectral analog of Selberg's result on $S(t)$. https://arxiv.org/abs/2410.03473

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