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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
DOI: https://doi.org/10.1090/S0025-5718-1985-0804950-3
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.


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DOI: https://doi.org/10.1090/S0025-5718-1985-0804950-3
Article copyright: © Copyright 1985 American Mathematical Society