Uniform distribution of polynomially-defined additive function to varying moduli

In 1969, Delange has proved a general criterion for uniform distribution of additive functions. In this paper, we study the uniform distribution of a special class of polynomially-defined additive functions where the moduli is allowed to vary. This paper takes inspiration from a similar paper that studies the distribution of some special multiplicative functions by Pollack and Singha Roy. The approach would require techniques in the paper mentioned and bound on exponential sums from Cochrane and Loh.