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Small Sets of k-th Powers

Published online by Cambridge University Press:  20 November 2018

Ping Ding  and
A. R. Freedman
Ping Ding
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, V5A 1S6
A. R. Freedman
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, V5A 1S6
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Abstract

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Let k ≥ 2 and q = g(k) — G(k), where g(k) is the smallest possible value of r such that every natural number is the sum of at most r k-th powers and G(k) is the minimal value of r such that every sufficiently large integer is the sum of r k-th powers. For each positive integer r ≥ q, let Then for every ε > 0 and N ≥ N(r, ε), we construct a set A of k-th powers such that |A| ≤ (r(2 + ε)r + l)N 1/(k+r) and every nonnegative integer n ≤ N is the sum of k-th powers in A. Some related results are also obtained.

Keywords

11P05

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 2 , 01 June 1994 , pp. 168 - 173
Copyright
Copyright © Canadian Mathematical Society 1994

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