Binary linear forms over finite sets of integers
数论
2021-01-06 v1 组合数学
摘要
Let A be a finite set of integers. For a polynomial f(x_1,...,x_n) with integer coefficients, let f(A) = {f(a_1,...,a_n) : a_1,...,a_n \in A}. In this paper it is proved that for every pair of normalized binary linear forms f(x,y)=u_1x+v_1y and g(x,y)=u_2x+v_2y with integral coefficients, there exist arbitrarily large finite sets of integers A and B such that |f(A)| > |g(A)| and |f(B)| < |g(B)|.
引用
@article{arxiv.math/0701001,
title = {Binary linear forms over finite sets of integers},
author = {Melvyn B. Nathanson and Kevin O'Bryant and Brooke Orosz and Imre Ruzsa and Manuel Silva},
journal= {arXiv preprint arXiv:math/0701001},
year = {2021}
}
备注
20 pages