Fourier uniformity of bounded multiplicative functions in short intervals on average
Terence Tao; Kaisa Matomäki; Maksym Radziwiłł
Fourier uniformity of bounded multiplicative functions in short intervals on average
Terence Tao
Kaisa Matomäki
Maksym Radziwiłł
Springer New York LLC
Julkaisun pysyvä osoite on:
https://urn.fi/URN:NBN:fi-fe2021042825307
https://urn.fi/URN:NBN:fi-fe2021042825307
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
Kokoelmat
- Rinnakkaistallenteet [19206]