34 citations · 268 across the 120 of their papers we have counts for
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Quantum integers and cyclotomy
Alexander Borisov, Yang Wang, Melvyn B. Nathanson
A sequence of functions {f_n(q)}_{n=1}^{\infty} satisfies the functional equation for multiplication of quantum integers if f_{mn}(q) = f_m(q)f_n(q^m) for all positive integers m a…
The inverse problem for representation functions of additive bases
Melvyn B. Nathanson
Let A be a set of integers. For every integer n, let r_{A,2}(n) denote the number of representations of n in the form n = a_1 + a_2, where a_1 and a_2 are in A and a_1 \leq a_2. Th…
On the ubiquity of Sidon sets
Melvyn B. Nathanson
A Sidon set is a set A of integers such that no integer has two essentially distinct representations as the sum of two elements of A. More generally, for every positive integer g,…
Formal power series arising from multiplication of quantum integers
Melvyn B. Nathanson
For the quantum integer [n]_q = 1+q+q^2+... + q^{n-1} there is a natural polynomial multiplication such that [mn]_q = [m]_q \otimes_q [n]_q. This multiplication is given by the fun…
Generalized additive bases, Konig's lemma, and the Erdos-Turan conjecture
Melvyn B. Nathanson
Let A be a set of nonnegative integers. For every nonnegative integer n and positive integer h, let r_{A}(n,h) denote the number of representations of n in the form n = a_1 + a_2 +…
Every function is the representation function of an additive basis for the integers
Melvyn B. Nathanson
Let A be a set of integers. For every integer n, let r_{A,h}(n) denote the number of representations of n in the form n = a_1 + a_2 + ... + a_h, where a_1, a_2,...,a_h are in A and…