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Bounds on Autocorrelation Coefficients of Rudin-Shapiro Polynomials

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Abstract

We study the autocorrelation coefficients of the Rudin–Shapiro polynomials, proving in particular that their maximum on the interval [1, 2n) is bounded from below by C12αn and is bounded from above by C22α’n where α = 0.7302852 ... and α′ = 0.7302867....

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Acknowledgement

The authors wish to acknowledge the anonymous reviewers for reviewing the paper, including the computational details, thoroughly.

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Authors and Affiliations

  1. CNRS, IMJ-PRG, Sorbonne Université, 4 Place Jussieu, Case 247, F-75252, Paris Cedex 05, France

    J.-P. Allouche

  2. Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, V5A 1S6, Canada

    S. Choi

  3. LRI et I2BC Université Paris-Sud, CNRS, Université Paris-Saclay, F-91405, Orsay Cedex, France

    A. Denise

  4. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA

    T. Erdélyi

  5. Départment de Mathématiques, Faculté des Sciences d’Orsay, Université Paris-Sud, F-91405, Orsay Cedex, France

    B. Saffari

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  1. J.-P. Allouche
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  2. S. Choi
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  3. A. Denise
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  4. T. Erdélyi
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  5. B. Saffari
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Correspondence to T. Erdélyi.

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Dedicated to the memory of Professor Jean-Pierre Kahane

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Allouche, JP., Choi, S., Denise, A. et al. Bounds on Autocorrelation Coefficients of Rudin-Shapiro Polynomials. Anal Math 45, 705–726 (2019). https://doi.org/10.1007/s10476-019-0003-4

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  • DOI: https://doi.org/10.1007/s10476-019-0003-4

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