Some algebraically independent continued fractions
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- by Vichian Laohakosol and Patchara Ubolsri PDF
- Proc. Amer. Math. Soc. 95 (1985), 169-173 Request permission
Abstract:
Using simple arguments, we prove algebraic independence of a class of continued fractions extending an earlier result of Bundschuh. We then apply it to give another proof of algebraic independence of numbers whose $g$-adic and continued fraction expansions are explicitly known.References
- William W. Adams and J. L. Davison, A remarkable class of continued fractions, Proc. Amer. Math. Soc. 65 (1977), no. 2, 194–198. MR 441879, DOI 10.1090/S0002-9939-1977-0441879-4
- Peter Bundschuh, Über eine Klasse reeller transzendenter Zahlen mit explizit angebbarer $g$-adischer und Kettenbruch-Entwicklung, J. Reine Angew. Math. 318 (1980), 110–119 (German). MR 579386, DOI 10.1515/crll.1980.318.110
- Peter Bundschuh, Transcendental continued fractions, J. Number Theory 18 (1984), no. 1, 91–98. MR 734440, DOI 10.1016/0022-314X(84)90045-3
- Alain Durand, Indépendance algébrique de nombres complexes et critère de transcendance, Compositio Math. 35 (1977), no. 3, 259–267 (French). MR 457364
- Yuval Z. Flicker, Algebraic independence by a method of Mahler, J. Austral. Math. Soc. Ser. A 27 (1979), no. 2, 173–188. MR 531112 G. H. Hardy and E. M. Wright, An introduction to the theory of numbers (4th ed.), Oxford Univ. Press, London, 1971.
- Iekata Shiokawa, Algebraic independence of certain gap series, Arch. Math. (Basel) 38 (1982), no. 5, 438–442. MR 666917, DOI 10.1007/BF01304813
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 169-173
- MSC: Primary 11J72; Secondary 11J70
- DOI: https://doi.org/10.1090/S0002-9939-1985-0801317-0
- MathSciNet review: 801317