The Shifted Convolution of Generalized Divisor Functions

Abstract

We prove an asymptotic formula for the shifted convolution of the divisor functions |$d_k(n)$| and |$d(n)$| with |$k \geq 4$|⁠, which is uniform in the shift parameter and which has a power saving error term, improving results obtained previously by Fouvry and Tenenbaum and, more recently, by Drappeau.