eng
episciences.org
Hardy-Ramanujan Journal
2804-7370
2013-01-01
Volume 34-35 - 2013
10.46298/hrj.2013.174
174
journal article
On Ramachandra's Contributions to Transcendental Number Theory
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.
https://hrj.episciences.org/174/pdf
four exponentials conjecture
Transcendental numbers
elliptic functions
additive functions
six exponentials theorem
Hilbert�s seventh problem
[MATH] Mathematics [math]