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Journal | Acta Arithmetica |
---|---|

Date | In preparation - 25 Jul 2015 |

Date | Accepted/In press - 25 Jul 2016 |

Date | E-pub ahead of print (current) - 22 Feb 2017 |

Issue number | 4 |

Volume | 177 |

Number of pages | 14 |

Early online date | 22/02/17 |

Original language | English |

For any j_1,...,j_n>0 with j_1+...+j_n=1 and any x \in R^n, we consider the
set of points y \in R^n for which max_{1\leq i\leq n}(||qx_i-y_i||^{1/j_i})>c/q
for some positive constant c=c(y) and all q\in N. These sets are the `twisted'
inhomogeneous analogue of Bad(j_1,...,j_n) in the theory of simultaneous
Diophantine approximation. It has been shown that they have full Hausdorff
dimension in the non-weighted setting, i.e provided that j_i=1/n, and in the
weighted setting when x is chosen from Bad(j_1,...,j_n). We generalise these
results proving the full Hausdorff dimension in the weighted setting without
any condition on x.

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- math.NT

## Programme Grant-New Frameworks in metric Number Theory

Project: Research

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