Correlations of the divisor function

Abstract

In 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).

arXiv comment33 pages. Corrections and journal reference

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• Generalised divisor sums of binary forms over number fields