Symon Serbenyuk
Published 2017-02-01Version 1
The article is devoted to the investigation of representation of rational numbers by Cantor series. Necessary and sufficient conditions for a rational number to be representable by a positive Cantor series are formulated for the case of an arbitrary sequence $(q_k)$ and some its corollaries are considered. Results of this article were presented by the author of this article on the International Conference on Algebra dedicated to 100th anniversary of S. M. Chernikov (www.researchgate.net/publication/311415815, www.researchgate.net/publication/301849984). This investigation was also presented in some reports (links to the reports: www.researchgate.net/publication/303736670, www.researchgate.net/publication/303720573, etc.).
Approximation of rational numbers by Dedekind sums
Towards the (ir)rationality of values of Dirichlet series
Some sufficient conditions of a given series with rational terms converging to an irrational number or a transcdental number
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