About: Six exponentials theorem

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In mathematics, specifically transcendental number theory, the six exponentials theorem is a result that, given the right conditions on the exponents, guarantees the transcendence of at least one of a set of exponentials.

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rdfs:label	Théorème des six exponentielles (fr) Six exponentials theorem (en)
rdfs:comment	In mathematics, specifically transcendental number theory, the six exponentials theorem is a result that, given the right conditions on the exponents, guarantees the transcendence of at least one of a set of exponentials. (en) En mathématiques, et plus spécialement dans la théorie des nombres transcendants, le théorème des six exponentielles, publié par Serge Lang et Kanakanahalli Ramachandra dans les années 1960, garantit, sous certaines conditions, l'existence d'au moins un nombre transcendant parmi six nombres écrits sous forme exponentielle. Ce théorème permet donc de prouver la transcendance d'un nombre, en mettant en évidence qu'il fait partie de six nombres vérifiant les hypothèses du théorème, dès lors que les cinq autres sont algébriques. (fr)
foaf:depiction
dcterms:subject	Conjectures Theorems in number theory Transcendental numbers Exponentials
Wikipage page ID	15114520 (xsd:integer)
Wikipage revision ID	1124317718 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Carl Ludwig Siegel Homomorphism Paul Erdős Vector space Conjectures Theorems in number theory Complex logarithm Complex numbers Transcendental numbers Mathematics Matrix (mathematics) Elliptic-curve cryptography Leonidas Alaoglu Colossally abundant number Acta Arithmetica Exponentials Transcendental number Addison-Wesley Algebraic number Field (mathematics) Four exponentials conjecture Journal of Number Theory Rank (linear algebra) Baker's theorem Prime number Kanakanahalli Ramachandra Integer Rational numbers Real number Semiprime Serge Lang Michel Waldschmidt Image (mathematics) Linearly independent Transcendental number theory Transactions of the American Mathematical Society Group variety
sameAs	Six exponentials theorem Six exponentials theorem Six exponentials theorem Six exponentials theorem Six exponentials theorem
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thumbnail	wiki-commons:Special:FilePath/N-Exponentials_Conjecture.png?width=300
title	Six exponentials theorem (en)
urlname	SixExponentialsTheorem (en)
has abstract	En mathématiques, et plus spécialement dans la théorie des nombres transcendants, le théorème des six exponentielles, publié par Serge Lang et Kanakanahalli Ramachandra dans les années 1960, garantit, sous certaines conditions, l'existence d'au moins un nombre transcendant parmi six nombres écrits sous forme exponentielle. Ce théorème permet donc de prouver la transcendance d'un nombre, en mettant en évidence qu'il fait partie de six nombres vérifiant les hypothèses du théorème, dès lors que les cinq autres sont algébriques. Il existe de nombreuses variantes de ce théorème, dont certaines sont encore des conjectures. Le diagramme ci-contre montre les implications logiques entre tous ces résultats ou conjectures. (fr) In mathematics, specifically transcendental number theory, the six exponentials theorem is a result that, given the right conditions on the exponents, guarantees the transcendence of at least one of a set of exponentials. (en)

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