A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Fourier uniformity of bounded multiplicative functions in short intervals on average
Tekijät: Kaisa Matomäki, Maksym Radziwiłł, Terence Tao
Kustantaja: Springer New York LLC
Julkaisuvuosi: 2020
Journal: Inventiones Mathematicae
Tietokannassa oleva lehden nimi: Inventiones Mathematicae
Vuosikerta: 220
Aloitussivu: 1
Lopetussivu: 58
eISSN: 1432-1297
DOI: https://doi.org/10.1007/s00222-019-00926-w(external)
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/44132506(external)
Let λ denote the Liouville function. We show that as X→∞ ,
∫2XXsupα∣∣∣∣∑x
for all H≥Xθ with θ>0 fixed but arbitrarily small. Previously, this was only known for θ>5/8 . For smaller values of θ this is the first “non-trivial” case of local Fourier uniformity on average at this scale. We also obtain the analogous statement for (non-pretentious) 1-bounded multiplicative functions. We illustrate the strength of the result by obtaining cancellations in the sum of λ(n)Λ(n+h)Λ(n+2h) over the ranges h
Ladattava julkaisu This is an electronic reprint of the original article. |