Short Exponential Sums and Ternary Correlations of Multiplicative Functions

Abstract

In this paper, we investigate the average behavior of ternary correlations for general $k$-divisor-bounded multiplicative functions, assuming certain second moment integral bounds for the associated $L$-functions. Our approach differs from previous methods based on spectral theory or Heath-Brown-type decompositions, and instead combines the circle method with weighted short exponential-sum bounds. The key input is short exponential-sum estimates obtained from integral moment bounds for $L$-functions.