Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Quantitative transcendence results for numbers associated with Liouville numbers

Author: Deanna M. Caveny
Journal: Proc. Amer. Math. Soc. 120 (1994), 349-357
MSC: Primary 11J82; Secondary 11J85
MathSciNet review: 1165048
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In 1937, Franklin and Schneider generalized the Gelfond-Schneider result on the transcendence of $ {\alpha ^\beta }$. They proved the following theorem: If $ \beta $ is an algebraic, irrational number and $ \alpha $ is "suitably well-approximated by algebraic numbers of bounded degree", then $ {\alpha ^\beta }$ is transcendental. In 1964, Feldman established the algebraic independence of $ \alpha $ and $ {\alpha ^\beta }$ under similar conditions. We use results concerning linear forms in logarithms to give quantitative versions of the Franklin-Schneider and Feldman results.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11J82, 11J85

Retrieve articles in all journals with MSC: 11J82, 11J85

Additional Information

Keywords: Quantitative, transcendence, Liouville numbers
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society