English

Bounds on Autocorrelation Coefficients of Rudin-Shapiro Polynomials

Classical Analysis and ODEs 2021-03-23 v2

Abstract

We study the autocorrelation coefficients of the Rudin-Shapiro polynomials, proving in particular that their maximum on the interval [1,2n)[1, 2^n) is bounded from below by C12αnC_1 2^{\alpha n} and is bounded from above by C22αnC_2 2^{\alpha' n} where α=0.7302852...\alpha = 0.7302852... and α=0.7302867...\alpha' = 0.7302867....

Keywords

Cite

@article{arxiv.1901.06832,
  title  = {Bounds on Autocorrelation Coefficients of Rudin-Shapiro Polynomials},
  author = {J. -P. Allouche and S. Choi and A. Denise and T. Erdélyi and B. Saffari},
  journal= {arXiv preprint arXiv:1901.06832},
  year   = {2021}
}