Schanuel's Conjecture and the Transcendence of Power Towers

dc.rights.license	CC BY	eng
dc.contributor.author	Trojovská, Eva	cze
dc.contributor.author	Trojovský, Pavel	cze
dc.date.accessioned	2025-12-05T09:58:50Z
dc.date.available	2025-12-05T09:58:50Z
dc.date.issued	2021	eng
dc.identifier.issn	2227-7390	eng
dc.identifier.uri	http://hdl.handle.net/20.500.12603/1247
dc.description.abstract	We give three consequences of Schanuel's Conjecture. The first is that P(e)(Q(e)) and P(pi)(Q(pi)) are transcendental, for any non-constant polynomials P(x),Q(x) is an element of Q vertical bar x vertical bar. The second is that pi not equal alpha(beta), for any algebraic numbers alpha and beta. The third is the case of the Gelfond's conjecture (about the transcendence of a finite algebraic power tower) in which all elements are equal.	eng
dc.format	p. "Article Number: 717"	eng
dc.language.iso	eng	eng
dc.publisher	MDPI-Molecular diversity preservation international	eng
dc.relation.ispartof	Mathematics, volume 9, issue: 7	eng
dc.subject	Schanuel's Conjecture	eng
dc.subject	Gelfond-Schneider Theorem	eng
dc.subject	Hermite-Lindemann Theorem	eng
dc.subject	algebraic independence	eng
dc.subject	transcendence degree	eng
dc.subject	power tower	eng
dc.title	Schanuel's Conjecture and the Transcendence of Power Towers	eng
dc.type	article	eng
dc.identifier.obd	43877675	eng
dc.identifier.doi	10.3390/math9070717	eng
dc.publicationstatus	postprint	eng
dc.peerreviewed	yes	eng
dc.source.url	https://www.mdpi.com/2227-7390/9/7/717	cze
dc.relation.publisherversion	https://www.mdpi.com/2227-7390/9/7/717	eng
dc.rights.access	Open Access	eng