Correlations of the divisor function

Matthiesen, LilianLilianMatthiesen2024-07-192024-07-192010-10-29https://resolver.sub.uni-goettingen.de/purl?gro-2/144312In this paper we study linear correlations of the divisor function tau(n) = sum_{d|n} 1 using methods developed by Green and Tao. For example, we obtain an asymptotic for sum_{n,d} tau(n) tau(n+d) ... tau(n+ (k-1)d).Correlations of the divisor functionjournal_article10.1112/plms/pdr046http://arxiv.org/abs/1011.0019v4