Abstract
We study the Fourier-Walsh spectrum \(\{ \widehat \mu (S);S \subset \{ 1, \ldots n\} \} \) of the Moebius function µ restricted to {0, 1, 2, …, 2n − 1} ≅ {0, 1}n and prove that it is not captured by levels \(\{ \widehat \mu (S):|S| < \rho n\} \), with ρ a sufficiently small constant. This improves the author’s earlier result in [B2].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Balog and A. Perelli, On the L 1 -mean of the exponential sum formed with the Möbius function, J. London Math. Soc. (2), 57 (1998), 275–288.
E. Bombieri, Le grand crible dans la théorie analytique des nombres, Astérisque 18 (1987).
J. Bourgain, Prescribing the binary digits of the primes, II, Israel J.Math 206 (2015), 165–182.
J. Bourgain, On the Fourier-Walsh spectrum of the Moebius function, Israel J. Math. 197 (2013), 215–235.
H. Iwaniec, On zeros of Dirichlet L series, Invent. Math. 23 (1974), 97–104.
H. Iwaniec and E. Kowalski, Analytic Number Theory, American Mathematical Society, Providence, RI, 2004.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bourgain, J. On the Fourier-Walsh spectrum of the Moebius function, II. JAMA 128, 355–367 (2016). https://doi.org/10.1007/s11854-016-0012-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11854-016-0012-1