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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
DOI: https://doi.org/10.1090/S0002-9939-1990-1007514-8
MathSciNet review: 1007514
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1007514-8
Article copyright: © Copyright 1990 American Mathematical Society