Abstract
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 |
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Approximation lattices of p-adic numbers. / Weger, de, B.M.M.
In: Journal of Number Theory, Vol. 24, No. 1, 1986, p. 70-88.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Approximation lattices of p-adic numbers
AU - Weger, de, B.M.M.
PY - 1986
Y1 - 1986
N2 - 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.
AB - 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.
U2 - 10.1016/0022-314X(86)90059-4
DO - 10.1016/0022-314X(86)90059-4
M3 - Article
VL - 24
SP - 70
EP - 88
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
IS - 1
ER -