### Abstract

Original language | English |
---|---|

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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*Journal of Number Theory*, vol. 24, no. 1, pp. 70-88. https://doi.org/10.1016/0022-314X(86)90059-4

**Approximation lattices of p-adic numbers.** / Weger, de, B.M.M.

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 -