Moebius-Walsh correlation bounds and an estimate of Mauduit and Rivat
Number Theory
2011-09-14 v1
Abstract
We establish small correlation bounds for the Moebius function and the Walsh system, answering affirmatively a question posed by G.Kalai [Ka]. The argument is based on generalizing the approach of Mauduit and Rivat [M-R] in order to treat Walsh functions of `large weight', while the `small weight' case follows from recent work due to B.Green [Gr]. The conclusion is an estimate uniform over the full Walsh system. A similar result also holds for the Liouville function.
Keywords
Cite
@article{arxiv.1109.2784,
title = {Moebius-Walsh correlation bounds and an estimate of Mauduit and Rivat},
author = {Jean Bourgain},
journal= {arXiv preprint arXiv:1109.2784},
year = {2011}
}