M. Nathanson

activity

20002026

most citedUnique representation bases for the integers

34 citations · 268 across the 120 of their papers we have counts for

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Showing 2022 · math.NTShow all

4 papers · 2 filters

math.NT2022

Exponential automorphisms and a problem of Mycielski

Melvyn B. Nathanson

An exponential automorphism of $C$ is a function $α : C \to C$ such that $α (z_{1} + z_{2}) = α (z_{1}) + α (z_{2})$ and $α (e^{z}) = e^{α (z)}$ for…

math.NT2022

Increasing-decreasing patterns in the iteration of an arithmetic function

Melvyn B. Nathanson

Let $Ω$ be a set of positive integers and let $f : Ω \to Ω$ be an arithmetic function. Let $V = (v_{i})_{i = 1}^{n}$ be a finite sequence of positive integers. An integer $m \in Ω$ …

math.NT2022

Interactions of zeros of of polynomials and multiplicity matrices

Melvyn B. Nathanson

An $m \times (n + 1)$ multiplicity matrix is a matrix $M = (μ_{i, j})$ with rows enumerated by $i \in {1, 2, \dots, m}$ and columns enumerated by $j \in {0, 1, \dots, n}$ w…

math.NT2022★ 7 cited

Underapproximation by Egyptian fractions

Melvyn B. Nathanson

An increasing sequence $(x_{i})_{i = 1}^{n}$ of positive integers is an $n$ -term Egyptian underapproximation of $θ \in (0, 1]$ if $\sum_{i = 1}^{n} \frac{1}{x _{i}} < θ$ . A greedy algorithm const…