Arindam Roy
UNC Charlotte
Title
Divisor-bounded multiplicative functions in arithmetic progressions
Abstract
In this work, we establish a mean-value estimate for trilinear forms involving arbitrary sequences over arithmetic progressions, after excluding the contribution of exceptional characters. Our result requires only minimal hypotheses on the growth of the sequences, and we provide upper bounds in terms of the $L^2$-norms of the corresponding sequences. As an application, we obtain a Bombieri-Vinogradov type theorem for a broad class of multiplicative functions supported on smooth numbers. In particular, we show that these functions are equidistributed in arithmetic progressions on average over moduli $q≤x^{3/5}−\epsilon$, provided they satisfy a Siegel-Walfisz criterion. This is joint work with Aditi Savalia and Akshaa Vatwani.