On Ramachandra's contributions to transcendental number theory

Michel Waldschmidt (1)

1 IMJ - Institut de Mathématiques de Jussieu

The title of this lecture refers to Ramachandra's paper in Acta Arithmetica [Ramachandra, 1968], which will be our central subject: in section 1 we state his Main Theorem, in section 2 we apply it to algebraically additive functions. Next we give new consequences of Ramachandra's results to density problems; for instance we discuss the following question: {\sl let $E$ be an elliptic curve which is defined over the field of algebraic numbers, and let $\Gamma$ be a finitely generated subgroup of algebraic points on $E$; is $\Gamma$ dense in $E(\bC)$ for the complex topology?} The other contributions of Ramachandra to transcendental number theory are dealt with more concisely in section 4. Finally we propose a few open problems.

Mots clés: transcendental number theory; Schneider's method

Domaines: Théorie des nombres [math.NT]

Michel Waldschmidt. On Ramachandra's contributions to transcendental number theory. The Riemann zeta function and related themes: papers in honour of Professor K. Ramachandra, National Institute for Advanced Studies (NIAS), Dec 2003, Bangalore, India. pp.155--179. ⟨hal-00411418⟩