Akshaa.Vatwani

Affiliation: IIT Gandhinagar

Title Of Talk: Divisor-bounded multiplicative functions in arithmetic progressions

Abstract: We establish a general 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 prove 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 $q \le x^{3/5-\varepsilon}$, if they satisfy a Siegel-Walfisz criterion.

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