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 $k\ge 4$, 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.

References in corpus (1)

• On a certain additive divisor problem

Cited by in corpus (5)

• Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges
• Combinatorial identities and Titchmarsh's divisor problem for multiplicative functions
• Uniform Titchmarsh divisor problems
• Large sieve inequalities for exceptional Maass forms and the greatest prime factor of $n^2+1$
• Mean values of long Dirichlet polynomials with divisor coefficients