On the arcsine law on divisors in arithmetic progressions

Suppose qq is not a Siegel ‘exceptional’ modulus and let εε be sufficiently small positive constant, in this paper, we show that the arcsine law on divisors holds in arithmetic progressions for q⩽exp{(14−ε)(log2x)2}, which generalizes the known result investigated by Deshouillers, Dress & Tenenbaum.