The algebraic independence of certain Liouville continued fractions

Adams, William W.

doi:10.1090/S0002-9939-1985-0810154-2

The algebraic independence of certain Liouville continued fractions
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Proc. Amer. Math. Soc. 95 (1985), 512-516 Request permission

Abstract:

This work uses some simple Liouville type arguments to extend some recent work of Bundschuh and of Laohakosol and Ubolsri on algebraic independence. The results are stronger and are not restricted to just two numbers. We then use the results to give a new and simple proof of Bundschuh’s result concerning the algebraic independence of certain numbers whose $g$-adic and continued fraction expansions are both known.

References

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Results concerning the algebraic independence of sets of Liouville numbers

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