Correlations of the von Mangoldt and higher divisor functions II: divisor correlations in short ranges
Terence Tao; Kaisa Matomäki; Maksym Radziwiłł
Correlations of the von Mangoldt and higher divisor functions II: divisor correlations in short ranges
Terence Tao
Kaisa Matomäki
Maksym Radziwiłł
Springer New York LLC
Julkaisun pysyvä osoite on:
https://urn.fi/URN:NBN:fi-fe20201209100129
https://urn.fi/URN:NBN:fi-fe20201209100129
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=(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
.
Kokoelmat
- Rinnakkaistallenteet [19207]