Approximation by Polynomials with Coefficients ±1

Yuval Peres; Boris Solomyak

doi:10.1006/jnth.2000.2514

Approximation by Polynomials with Coefficients ±1

Yuval Peres
, Boris Solomyak

Hebrew University of Jerusalem
University of California at Berkeley
University of Washington

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	185-198
Number of pages	14
Journal	Journal of Number Theory
Volume	84
Issue number	2
DOIs	https://doi.org/10.1006/jnth.2000.2514
State	Published - Oct 2000
Externally published	Yes

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

Funders	Funder number
Directorate for Mathematical and Physical Sciences	9800786, 9803597

Keywords

Pisot numbers
Polynomial approximation
digit expansions

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10.1006/jnth.2000.2514

Cite this

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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.",

keywords = "Pisot numbers, Polynomial approximation, digit expansions",

author = "Yuval Peres and Boris Solomyak",

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

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AU - Solomyak, Boris

N1 - Funding Information: 1Research partially supported by NSF Grant DMS-9803597. 2Research supported in part by NSF Grant DMS 9800786 and the Fulbright foundation.

PY - 2000/10

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N2 - 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.

AB - 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.

KW - Pisot numbers

KW - Polynomial approximation

KW - digit expansions

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Approximation by Polynomials with Coefficients ±1

Abstract

Bibliographical note

Funding

Keywords

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