Correlations of the divisor function

Details Correlations of the divisor function Correlations of the divisor function

2010-10-29

arxiv.org/abs/1011.0019v3

Mathematics

Number Theory

33 pages

Scientific paper

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).

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