Qing-Feng Sun

A $\mathrm{GL}_3$ level analog of Selberg's result for $S(t)$

Let $\pi$ be a spherical cuspidal $\mathrm{GL}_3$ newform of prime level $N$ and trivial central character, and define $S(t,\pi)=\pi^{-1}\arg L(1/2+\textrm{i}t,\pi)$. Assuming the generalized Riemann hypothesis for $L(s,\pi)$, we establish an asymptotic formula for each fixed weighted moment of $S(t,\pi)$ as $N\to\inft...