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On Ramachandra’s contributions to transcendental number theory. (English) Zbl 1162.11038

Balasubramanian, R. (ed.) et al., The Riemann zeta function and related themes. Papers in honour of Professor K. Ramachandra. Proceedings of the international conference on analytic number theory, Bangalore, India, December 13–15, 2003. Mysore: Ramanujan Mathematical Society (ISBN 978-81-902545-2-6/pbk). Ramanujan Mathematical Society Lecture Notes Series 2, 155-179 (2006).
The main thema of this survey is K. Ramachandra’s Main Theorem [Acta Arith. 14, 65–72, 73–88 (1968; Zbl 0176.33101)]. This very general and important result in transcendental number theory uses Schneider’s method. This theorem is applied to algebraically additive functions. Then the author gives new consequences of this theorem to density problems, for example: let \(E\) be an elliptic curve defined over the field of algebraic numbers and let \(\Gamma\) be a finitely generated subgroup of algebraic points of \(E\); is \(\Gamma\) dense in \(E({\mathbf C})\) for the usual complex topology? Then, the other contributions of Ramachandra to transcendental number theory are dealt with more consisely. The paper ends with a few open problems, for example: improve on the present effective versions of Ramachandra’s Main Theorem.
For the entire collection see [Zbl 1113.00006].

MSC:

11J81 Transcendence (general theory)

Citations:

Zbl 0176.33101
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