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- W4387560112 abstract "Let $tinN$ and let $lio$ denote the Liouville function. We show that $$lim_{Htoinfty}limsup_{Mtoinfty}EE^{rm log}_{mleq M}sup_{alphain C}big|EE_{hleq H}lio(m+h)e^{2pi ih^talpha}big|=0$$ holds in the case $t=1$ for all closed $CsubsetT$ of zero Lebesgue measure and in the case $tgeq 2$ for all closed $CsubsetT$ of upper box-counting dimension $<1/t$. We also consider a more uniform version of the general logarithmic local $t$-Fourier uniformity problem for the Liouville function and show that it holds for compact countable ergodic subsets of $t$-step nilpotent Lie groups. Furthermore, we discuss the Ces`aro version of the local $1$-Fourier uniformity problem, showing its validity for a class of ``rigid'' sets (of full Hausdorff dimension) and proving a density result for all closed subsets of zero Lebesgue measure." @default.
- W4387560112 created "2023-10-12" @default.
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- W4387560112 date "2023-10-09" @default.
- W4387560112 modified "2023-10-18" @default.
- W4387560112 title "On the local Fourier uniformity problem for small sets" @default.
- W4387560112 doi "https://doi.org/10.48550/arxiv.2310.05528" @default.
- W4387560112 hasPublicationYear "2023" @default.
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