Correlations of the von Mangoldt and higher divisor functions II: divisor correlations in short ranges - UTU Tutkimustietojärjestelmä

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

Tekijät: Kaisa Matomäki, Maksym Radziwiłł, Terence Tao

Kustantaja: Springer New York LLC

Julkaisuvuosi: 2019

Journal: Mathematische Annalen

Tietokannassa oleva lehden nimi: Mathematische Annalen

Vuosikerta: 374

Numero: 1-2

Aloitussivu: 793

Lopetussivu: 840

Sivujen määrä: 48

ISSN: 0025-5831

eISSN: 1432-1807

DOI: https://doi.org/10.1007/s00208-018-01801-4

Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/40056918

Tiivistelmä

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=(log⁡X)10000klog⁡k

, 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

.

Ladattava julkaisu

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CorrelationsII.pdf