Algebraic groups and small transcendence degree. II
type: Item
instance of: scholarly article
title: Algebraic groups and small transcendence degree. II
zbMATH Open document ID: 0712.11039
DOI: 10.1016/0022-314X(90)90107-3
author: Robert Tubbs
published in: Journal of Number Theory
publication date: 1990-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11J81
Mathematics Subject Classification ID: 11J85
Mathematics Subject Classification ID: 14L15
zbMATH DE Number: 4171025
zbMATH Keywords: transcendence degree
zbMATH Keywords: commutative algebraic groups
zbMATH Keywords: three algebraically independent numbers
zbMATH Keywords: linear independence
reviewed by: Michel Waldschmidt
MaRDI profile type: Publication
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full work available at URL: 0022-314x(90)90107-3
OpenAlex ID: W4205696848
description: scientific article; zbMATH DE number 4171025