Correlations of the von Mangoldt and higher divisor functions II. Divisor correlations in short ranges

Article, Preprint OPEN
Matomäki, Kaisa; Radziwiłł, Maksym; Tao, Terence;
(2019)
  • Publisher: Springer Verlag
  • Subject: Mathematics - Number Theory
    arxiv: Mathematics::Number Theory

We study the problem of obtaining asymptotic formulas for the sums $\sum_{X < n \leq 2X} d_k(n) d_l(n+h)$ and $\sum_{X < n \leq 2X} \Lambda(n) d_k(n+h)$, where $\Lambda$ is the von Mangoldt function, $d_k$ is the $k^{\operatorname{th}}$ divisor function, $X$ is large an... View more
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