On the solution of Waring Problem with a multiplicative error term: dimension free estimates
Jaros{\l}aw Mirek, Wojciech S{\l}omian, B{\l}a\.zej Wr\'obel
TL;DR
This paper establishes a dimension-free relation between radius and dimension for the Waring problem, providing asymptotic formulas that hold uniformly across dimensions with a multiplicative error term.
Contribution
It introduces a novel dimension-free estimate linking radius and dimension in the Waring problem with a multiplicative error term.
Findings
Derived a dimension-free asymptotic formula for the Waring problem.
Established a relation between radius and dimension independent of specific dimension.
Provided bounds that hold uniformly across different dimensions.
Abstract
We give a relation between the radius and the dimension in which the asymptotic formula in the Waring problem holds in a multiplicative and dimension-free fashion.
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Taxonomy
Topicsadvanced mathematical theories · Mathematical Analysis and Transform Methods · Matrix Theory and Algorithms