naa a22 4500 510781527 CHVBK 20180411083249.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1007/s11854-013-0005-2 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0005-2 Bourgain J. School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, 08540, Princeton, NJ, USA aut Möbius-Walsh correlation bounds and an estimate of Mauduit and Rivat [Elektronische Daten] [J. Bourgain] We establish small correlation bounds for the Möbius 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. Hebrew University Magnes Press, 2013 Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 147-163 0021-7670 119:1<147 2013 119 11854 https://doi.org/10.1007/s11854-013-0005-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0005-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bourgain J. School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, 08540, Princeton, NJ, USA aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 147-163 0021-7670 119:1<147 2013 119 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer