A note on some elementary measures of algebraic independence
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- by Robert Tubbs PDF
- Proc. Amer. Math. Soc. 109 (1990), 297-304 Request permission
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
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Additional Information
- © Copyright 1990 American Mathematical Society
- 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