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An explicit dense universal Hilbert set

Published online by Cambridge University Press:  20 June 2018

MICHAEL FILASETA  and
ROBERT WILCOX
MICHAEL FILASETA
Affiliation:
Department of Mathematics, LeConte College, 1523 Greene Street, University of South Carolina, Columbia, SC 29208U.S.A. e-mails: filaseta@math.sc.edu, rwilcox5@gmail.com
ROBERT WILCOX
Affiliation:
Department of Mathematics, LeConte College, 1523 Greene Street, University of South Carolina, Columbia, SC 29208U.S.A. e-mails: filaseta@math.sc.edu, rwilcox5@gmail.com
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Abstract

We provide the first explicit example of a universal Hilbert set ${\Ncal S}$ having asymptotic density 1 in the set of integers. More precisely, the number of integers not in ${\Ncal S}$ with absolute value ≤ X is bounded by X/(log X)δ, where δ = 1 − (1 + loglog 2)/(log 2) = 0.086071. . ..

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 167 , Issue 3 , November 2019 , pp. 531 - 547
Copyright
Copyright © Cambridge Philosophical Society 2018 

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