A1 Refereed original research article in a scientific journal
Correlations of the von Mangoldt and higher divisor functions II: divisor correlations in short ranges
Authors: Kaisa Matomäki, Maksym Radziwiłł, Terence Tao
Publisher: Springer New York LLC
Publication year: 2019
Journal: Mathematische Annalen
Journal name in source: Mathematische Annalen
Volume: 374
Issue: 1-2
First page : 793
Last page: 840
Number of pages: 48
ISSN: 0025-5831
eISSN: 1432-1807
DOI: https://doi.org/10.1007/s00208-018-01801-4
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/40056918
We study the problem of obtaining asymptotic formulas for the sums ∑ XX is large and k≥l≥2 k≥l≥2
are integers. We show that for almost all h∈[−H,H] h∈[−H,H]
with H=(logX) 10000klogk H=(logX)10000klogk
, the expected asymptotic estimate holds. In our previous paper we were able to deal also with the case of Λ(n)Λ(n+h) Λ(n)Λ(n+h)
and we obtained better estimates for the error terms at the price of having to take H=X 8/33+ε H=X8/33+ε
.
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