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

Abstract

Let $S_j(t)=\frac{1}{\ddot{I}}€\arg L(1/2+it,u_j)$, where $u_j$ is an even Hecke--Maass cusp form for $\mathrm{S}{\mathrm{L}}_2(\mathbb{Z})$ with Laplacian eigenvalue $\hat{I}{»}_j=\frac{1}{4}+t_j^2$. Without assuming the GRH, we establish an asymptotic formula for the moments of $S_j(t)$.

23 pages. Comments welcome!