Uniform distribution of some arithmetical functions

Abstract. We investigate the uniform distribution modulo 1 of sequence \({a(n)\over {b(n)}}~(n\in{\mathbb N})\), where \(a(n)\) and \(b(n)\) are suitable additive or multiplicative functions. We prove that if \(\kappa(n)\) is any of \({An^r\over {\omega (n)^h}},~ {An^r\over {a^{\omega (n)}}},~ {An^r\over {\tau (n^h)}}~~(r,h,A\in{\mathbb N})\) and \(f(n)\) is an arbitrary additive function, then \(\kappa(n)+f(n)\) is uniformly distributed mod 1.