{"docId":174,"paperId":174,"url":"https:\/\/hrj.episciences.org\/174","doi":"10.46298\/hrj.2013.174","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":45,"name":"Volume 34-35 - 2013"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01112588","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-01112588v1","dateSubmitted":"2015-03-03 16:14:05","dateAccepted":"2015-06-12 16:06:03","datePublished":"2013-01-01 08:00:00","titles":{"en":"On Ramachandra's Contributions to Transcendental Number Theory"},"authors":["Waldschmidt, Michel"],"abstracts":{"en":"The first part of this paper is a survey on Ramachandra's contribution to transcendental number theory included in his 1968 paper in Acta Arithmetica. It includes a discussion of pseudo-algebraic points of algebraically additive functions. The second part deals with applications to density statements related with a conjecture due to B.~Mazur. The next part is a survey of other contributions of Ramachandra to transcendence questions (on the numbers $2^{\\pi^k}$, a note on Baker's method, an easy transcendence measure for $e$). Finally, related open questions are raised."},"keywords":[["four exponentials conjecture"],["Transcendental numbers"],["elliptic functions"],["additive functions"],["six exponentials theorem"],["Hilbert\ufffds seventh problem"],"[MATH] Mathematics [math]"]}