A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä

Fourier uniformity of bounded multiplicative functions in short intervals on average




TekijätKaisa Matomäki, Maksym Radziwiłł, Terence Tao

KustantajaSpringer New York LLC

Julkaisuvuosi2020

JournalInventiones Mathematicae

Tietokannassa oleva lehden nimiInventiones Mathematicae

Vuosikerta220

Aloitussivu1

Lopetussivu58

eISSN1432-1297

DOIhttps://doi.org/10.1007/s00222-019-00926-w(external)

Rinnakkaistallenteen osoitehttps://research.utu.fi/converis/portal/detail/Publication/44132506(external)


Tiivistelmä

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

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Last updated on 2024-26-11 at 20:36