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)



A note on some elementary measures of algebraic independence

Author: Robert Tubbs
Journal: Proc. Amer. Math. Soc. 109 (1990), 297-304
MSC: Primary 11J85; Secondary 11J89
MathSciNet review: 1007514
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We investigate the algebraic independence of some numbers associated with elliptic functions when one of the numbers is a "Liouville-type" number. Suppose $ \wp (z)$ is a Weierstrass elliptic function with algebraic invariants and $ \beta $ is an algebraic number, not belonging to the field of multiplications for $ \wp (z)$. We establish the algebraic independence of $ \wp (u)$ and $ \wp (\beta u)$ (respectively, of $ u$ and $ \wp (\beta u)$) when $ \wp (u)$ (respectively, $ u$) is a "Liouville-type" number. We also give quantitative versions of these results.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11J85, 11J89

Retrieve articles in all journals with MSC: 11J85, 11J89

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society