CaltechAUTHORS
Published July 5, 2017 | Version Submitted
Discussion Paper Open

Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges

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Abstract

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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Identifiers

Eprint ID
87015
Resolver ID
CaltechAUTHORS:20180612-134458335

Related works

Describes
https://arxiv.org/abs/1707.01315 (URL)

Funding

Academy of Finland
285894
Natural Sciences and Engineering Research Council of Canada (NSERC)
Canada Research Chairs Program
Alfred P. Sloan Foundation
Simons Foundation
James and Carol Collins Chair
Mathematical Analysis and Application Research Fund Endowment
NSF
DMS-1266164
NSF
DMS-1440140

Dates

Created
2018-06-12
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Updated
2023-06-02
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