Research output: Contribution to journal › Article › peer-review

Journal | Mathematische Annalen |
---|---|

Date | E-pub ahead of print - 1 Mar 2014 |

Date | Published (current) - Aug 2014 |

Issue number | 3-4 |

Volume | 359 |

Number of pages | 55 |

Pages (from-to) | 969-1023 |

Early online date | 1/03/14 |

Original language | English |

Let C be two times continuously differentiable curve in R^2 with at least one point at which the curvature is non-zero. For any i,j > 0 with i+j =1, let Bad(i,j) denote the set of points (x,y) in R^2 for which max {||qx ||^{1/i}, ||qy||^{1/j}} > c/q for all integers q >0. Here c = c(x,y) is a positive constant. Our main result implies that any finite intersection of such sets with C has full Hausdorff dimension. This provides a solution to a problem of Davenport dating back to the sixties.

44 pages

- math.NT, 11J83, 11J13, 11K60

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