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June 2019 Weighted real Egyptian numbers
Melvyn B. Nathanson
Funct. Approx. Comment. Math. 60(2): 155-166 (June 2019). DOI: 10.7169/facm/1702

Abstract

Let $\mca = (A_1,\ldots, A_n)$ be a sequence of nonempty finite sets of positive real numbers, and let $\mcb = (B_1,\ldots, B_n)$ be a sequence of infinite discrete sets of positive real numbers. A \emph{weighted real Egyptian number with numerators $\mathcal{A}$ and denominators $\mathcal{B}$} is a real number $c$ that can be represented in the form \[ c = \sum_{i=1}^n \frac{a_i}{b_i} \] with $a_i \in A_i$ and $b_i \in B_i$ for $i \in \{1,\ldots, n\}$. In this paper, classical results of Sierpiński for Egyptian fractions are extended to the set of weighted real Egyptian numbers.

Citation

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Melvyn B. Nathanson. "Weighted real Egyptian numbers." Funct. Approx. Comment. Math. 60 (2) 155 - 166, June 2019. https://doi.org/10.7169/facm/1702

Information

Published: June 2019
First available in Project Euclid: 28 March 2018

zbMATH: 07068528
MathSciNet: MR3964257
Digital Object Identifier: 10.7169/facm/1702

Subjects:
Primary: 11D68 , 11D85
Secondary: 11A67 , 11B75

Keywords: Egyptian fractions , nowhere dense sets

Rights: Copyright © 2019 Adam Mickiewicz University

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Vol.60 • No. 2 • June 2019
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