Uniform bounds in Waring's problem over some diagonal forms

2020/10/27 by Pliego, Javier
#11E76 #11P05 #11P55 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2010.14567

Abstract

We investigate the existence of representations of every large positive integer as a sum of k-th powers of integers represented as certain diagonal forms. In particular, we consider a family of diagonal forms and discuss the problem of giving a uniform upper bound over the family for the number of variables needed to have such representations.

Related

• On Waring's problem in sums of three cubes
• On Waring's problem in sums of three cubes for smaller powers
• On Waring's problem for several homogeneous forms
• Expression for g(k) Related to Waring's Problem
• Integers that are not the sum of positive powers