TL;DR
This paper reviews classical methods for constructing thin bases of finite order in additive number theory, highlighting Cassels' polynomially asymptotic bases and discussing open problems in the field.
Contribution
It provides a comprehensive presentation of Cassels' construction of polynomially asymptotic bases and discusses related open problems in additive number theory.
Findings
Detailed exposition of Cassels' polynomial bases
Identification of open problems in thin bases construction
Clarification of classical constructions in additive number theory
Abstract
This paper describes several classical constructions of thin bases of finite order in additive number theory, and, in particular, gives a complete presentation of a beautiful construction of J. W. S. Cassels of a class of polynomially asymptotic bases. Some open problems are also discussed.
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Taxonomy
TopicsAnalytic Number Theory Research · Mathematics and Applications · Mathematical Dynamics and Fractals