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Published June 12, 2018 | Submitted
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Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges


We show that the expected asymptotic for the sums ∑_(X

Additional Information

KM was supported by Academy of Finland grant no. 285894. MR was supported by a NSERC Discovery Grant, the CRC program and a Sloan fellowship. TT was supported by a Simons Investigator grant, the James and Carol Collins Chair, the Mathematical Analysis & Application Research Fund Endowment, and by NSF grant DMS-1266164. We are indebted to Yuta Suzuki for a reference and for pointing out a gap in the proof of Proposition 5.1 in an earlier version of the paper. We also thank Sary Drappeau for comments on the introduction. Part of this paper was written while the authors were in residence at MSRI in Spring 2017, which is supported by NSF grant DMS-1440140.

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