Algebraic groups and small transcendence degree. II
This paper is a continuation of a previous article in the same journal [ibid. 25, 279-307 (1987; Zbl 0608.10036)]. The author's aim is to show that certain fields have transcendence degree at least two. These fields are generated by values of one-parameter subgroups of commutative algebraic groups. The refinements which are achieved in the present paper arise by assuming that certain values of the one parameter subgroup are algebraic. Four main theorems are given, and several corollaries are deduced; these corollaries concern the values of the usual exponential function together with elliptic functions. There are now similar results for large transcendence degree, but as soon as one wishes to produce at least three algebraically independent numbers, one usually needs a ``technical hypothesis'' (in the simplest case a measure of linear independence). The results of the present paper are especially elegant since they do not involve such an assumption, and nevertheless are far reaching.
scientific article; zbMATH DE number 4171025
scientific article