. This new
results provides several interesting corollaries, in particular, a
generalization of G. Diaz's refined Gelfond-Feldman measure to higher
dimensions and an improvement of Tubbs' elliptic Gelfond-Feldman
measure.
DEANNA M. CAVENY
The main theorem of this paper is a
measure of algebraic independence for numbers associated with a
one-parameter subgroup of a commutative algebraic group defined over
a number field. Qualitative results in this setting have been given
by M. Waldschmidt, R. Tubbs and M. Ably, who provided measures as
well. We refine Ably's quantitative results, separating the degree
and the height in the limit case when the group contains a copy of
the additive group of complex numbers, i.e., . This new
results provides several interesting corollaries, in particular, a
generalization of G. Diaz's refined Gelfond-Feldman measure to higher
dimensions and an improvement of Tubbs' elliptic Gelfond-Feldman
measure.