Approximation by Polynomials with Coefficients ±1

Yuval Peres, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

In response to a question of R. Kenyon, we prove that the set of polynomials with coefficients ±1, evaluated at a fixed real number θ, is dense in R for a.e. θ∈(2, 2). For θ∈(1, 2], a more complete result can be obtained by elementary methods.

Original languageEnglish
Pages (from-to)185-198
Number of pages14
JournalJournal of Number Theory
Volume84
Issue number2
DOIs
StatePublished - Oct 2000
Externally publishedYes

Bibliographical note

Funding Information:
1Research partially supported by NSF Grant DMS-9803597. 2Research supported in part by NSF Grant DMS 9800786 and the Fulbright foundation.

Funding

FundersFunder number
Directorate for Mathematical and Physical Sciences9800786, 9803597

    Keywords

    • Pisot numbers
    • Polynomial approximation
    • digit expansions

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