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# On Ramachandra's Contributions to Transcendental Number Theory

Abstract : 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.
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Cited literature [68 references]

https://hal.archives-ouvertes.fr/hal-01112588
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Submitted on : Tuesday, February 3, 2015 - 2:30:02 PM
Last modification on : Tuesday, March 29, 2022 - 3:58:51 AM
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34-35Article3.pdf
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### Citation

Michel Waldschmidt. On Ramachandra's Contributions to Transcendental Number Theory. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2013, Volume 34-35 - 2013, pp.18 - 46. ⟨10.46298/hrj.2013.174⟩. ⟨hal-01112588⟩

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