A Caltech Library Service

On sums of Rudin-Shapiro coefficients II

Brillhart, John and Erdős, Paul and Morton, Patrick (1983) On sums of Rudin-Shapiro coefficients II. Pacific Journal of Mathematics, 107 (1). pp. 39-69. ISSN 0030-8730.

See Usage Policy.


Use this Persistent URL to link to this item:


Let {a(n)} be the Rudin-Shapiro sequence, and let s(n) = ∑a(k) and t(n) = ∑(-1)k a(k). In this paper we show that the sequences {s(n)/√n} and {t(n)/√n} do not have cumulative distribution functions, but do have logarithmic distribution functions (given by a specific Lebesgue integral) at each point of the respective intervals [√3/5, √6] and [0, √3]. The functions a(x) and s(x) are also defined for real x ≥ 0, and the function [s(x) – a(x)]/√x is shown to have a Fourier expansion whose coefficients are related to the poles of the Dirichlet series ∑a(n)/n, where Re τ > ½.

Item Type:Article
Related URLs:
URLURL TypeDescription
Additional Information:© 1983 Pacific Journal of Mathematics. Received January 13, 1981. We would like to thank Igor Mikolic-Torreira for carrying out the computations in Table 1 (§6), and Richard Blecksmith for providing us with the graphs in Figure 1 (§4). We are also grateful to A.J.E.M. Janssen for his remarks concering several of our proofs.
Issue or Number:1
Record Number:CaltechAUTHORS:BRIpjm83
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2321
Deposited By: Tony Diaz
Deposited On:27 Mar 2006
Last Modified:02 Oct 2019 22:52

Repository Staff Only: item control page