Correlations of the divisor function

@article{Matthiesen2012CorrelationsOT,
  title={Correlations of the divisor function},
  author={Lilian Matthiesen},
  journal={Proceedings of The London Mathematical Society},
  year={2012},
  volume={104},
  pages={827-858}
}
  • Lilian Matthiesen
  • Published 2012
  • Mathematics
  • Proceedings of The London Mathematical Society
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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