On sums of Rudin-Shapiro coefficients II

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

The Vehicle, Fall 1993

Table of Contents 7/10ths SynthesisPeter F. Essigpage 5 Aug 1992 (My Small Catechism)Jon Montgomerypage 6 Chaos Is-J. Dylan McNeillpage 7 UntouchedTraci Williamspage 8 The JustificationJohn C. Carminepage 8 LincolnJon Montgomerypage 9 Untitled (Photo)Nicole Niemanpage 10 Park PoemJohn Brillhartpage 11 SmokeJulia Ann Canhampage 12 Warming the BenchAnn Moutraypage 12 Cereal KillerJay Harnackpage 13 The Dutiful SonsTom McGrathpage 14 UntitledCatherine DeGraafpage 17 7-up bottleWalt Howardpage 17 BreedDan Trutterpage 18 An Argument Against LoveTony Martinezpage 19 UntitledT. Scott Laniganpage 19 Glassblowers BallStephanie Franzenpage 20 Portrait of a Young GirlJohn C. Carminepage 20 Untitled (artwork)Dan Trutterpage 21 Death of a FriendLizabeth Kulkapage 22 Submission BluesMartin Paul Brittpage 23 To the Fourteen Year Old SuicideScott Langenpage 23 The Flabby PilgrimTom McGrathpage 24 The Fall of ImmortalityBrian Wheelerpage 25 Merging with AirThom Schnarrepage 26 UntitledCatherine DeGraafpage 27 Tree FishSandra Beauchamppage 28 Country SlumberJ. Dylan McNeillpage 29 Untitled (artwork)Dan Trutterpage 33 Authors\u27 Pagepage 34https://thekeep.eiu.edu/vehicle/1060/thumbnail.jp