Michel Waldschmidt - On Ramachandra's Contributions to Transcendental Number Theory

hrj:174 - Hardy-Ramanujan Journal, January 1, 2013, Volume 34-35 - https://doi.org/10.46298/hrj.2013.174
On Ramachandra's Contributions to Transcendental Number Theory

Authors: Michel Waldschmidt

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.

Volume: Volume 34-35
Published on: January 1, 2013
Submitted on: March 3, 2015
Keywords: four exponentials conjecture,Transcendental numbers, elliptic functions, additive functions, six exponentials theorem, Hilbert�s seventh problem,[MATH] Mathematics [math]


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