Two problems on the distribution of Carmichael's lambda function

Abstract

AbstractLet denote the exponent of the multiplicative group modulo n. We show that when q is odd, each coprime residue class modulo q is hit equally often by as n varies. Under the stronger assumption that , we prove that equidistribution persists throughout a Siegel–Walfisz‐type range of uniformity. By similar methods we show that obeys Benford's leading digit law with respect to natural density. Moreover, if we assume Generalized Riemann Hypothesis, then Benford's law holds for the order of a mod n, for any fixed integer .