Abstract We establish a result of Bombieri–Vinogradov type for the Dirichlet coefficients at prime ideals standard $L$-function associated to self-dual cuspidal automorphic representation $\pi $ $\operatorname {GL}_n$ over number field $F$ when $\pi$ is not quadratic twist itself. Our does rely on any unproven progress towards generalized Ramanujan conjecture or nonexistence Landau–Siegel zeros...

We study slow entropy invariants for abelian unipotent actions $ U on any finite volume homogeneous space G/\Gamma $. For every such action we show that the topological can be computed directly from dimension of a special decomposition {{\rm{Lie}}}(G) induced by {{\rm{Lie}}}(U) Moreover, are able to metric coincides with its entropy. As corollary, obtain complexity horocyclic is only related G ...