Abstract
Approximation lattices occur in a natural way in the study of rational approximations to p-adic numbers. Periodicity of a sequence of approximation lattices is shown to occur for rational and quadratic p-adic numbers, and for those only, thus establishing a p-adic analogue of Lagrange's theorem on periodic continued fractions. Using approximation lattices we derive upper and lower bounds for the best approximations to a p-adic number, thus establishing the p-adic analogue of a theorem of Hurwitz.
Original language | English |
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Pages (from-to) | 70-88 |
Number of pages | 19 |
Journal | Journal of Number Theory |
Volume | 24 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1986 |