On Liouville Numbers: Yet Another Application of Functional Analysis to Number Theory

Jörn Steuding ()
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Jörn Steuding: Würzburg University, Department of Mathematics

A chapter in From Arithmetic to Zeta-Functions, 2016, pp 485-507 from Springer

Abstract: Abstract In 1962, Erdős proved that every real number can be represented as a sum and as a product of two Liouville numbers. This has been generalized by Rieger and Schwarz. In this note we shall give an analysis of these results and their proofs. Moreover, we consider a certain subclass of Liouville numbers and prove similar results for this subclass. Since Wolfgang Schwarz had been very much interested in the history of mathematics, and the author shares this interest, he could not resist to include a few historical remarks (and footnotes) on transcendental numbers and Baire’s category theorem which might be interesting for the reader.

Keywords: Baire’s theorem; Liouville numbers; Primary 11J81; Secondary 54E52; 01A55 (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-28203-9_29

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DOI: 10.1007/978-3-319-28203-9_29

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