Density and finiteness results on sums of fractions

Autor:	Doğa Can Sertbaş, Haydar Göral
Přispěvatelé:	[Goral, Haydar] Dokuz Eylul Univ, Fac Sci, Dept Math, TR-35390 Tinaztepe Yerleskesi, Buca Izmir, Turkey -- [Sertbas, Doga Can] Cumhuriyet Univ, Dept Math, Fac Sci, TR-58140 Sivas, Turkey
Rok vydání:	2018
Předmět:	height function Pure mathematics Applied Mathematics General Mathematics quantitative estimates Egyptian fractions nonstandard analysis Algebraic number field number fields Egyptian fraction Height function Mathematics
Zdroj:	Proceedings of the American Mathematical Society. 147:567-581
ISSN:	1088-6826 0002-9939
DOI:	10.1090/proc/14270
Popis:	WOS: 000454742000015 We show that the height density of a finite sum of fractions is zero. In fact, we give quantitative estimates in terms of the height function. Then, we focus on the unit fraction solutions in the ring of integers of a given number field. In particular, we prove that finitely many representations of 1 as a sum of unit fractions determines the field of rational numbers among all real number fields. Finally, using non-standard methods, we prove some density and finiteness results on a finite sum of fractions. Nesin Mathematics Village The authors would like to thank Nesin Mathematics Village for their support and warm hospitality.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::11ee27e5c4b29585e367ecdbe2b2ced3 https://doi.org/10.1090/proc/14270 Zobrazit plný text záznamu