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A counterexample to a conjecture of Mahler on best $ p$-adic Diophantine approximation constants

Author: Alice A. Deanin
Journal: Math. Comp. 45 (1985), 621-632
MSC: Primary 11J61
MathSciNet review: 804950
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Abstract: In 1940, Mahler proposed a conjecture regarding the value of best P-adic Diophantine approximation constants. In this paper, a computational technique which tests the conjecture for any particular P is described. A computer search verified the conjecture for all $ P \leqslant 101$, except 83. The case P = 83 is discussed. A counterexample is given.

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

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  • [2] A. A. Deanin, Mahler's P-Adic Continued Fraction Algorithm, Ph.D. Dissertation, University of Maryland, 1983.
  • [3] A. A. Deanin, "Periodicity of P-adic continued fraction expansions." (Preprint). MR 846967 (87k:11072)
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Article copyright: © Copyright 1985 American Mathematical Society

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