## Abstract

Let α be an irrational number with bounded partial quotients of the continued fraction a_{k}. It is well known that symmetrizations of the irrational lattice have optimal order of L_{2} discrepancy, √log N. The same is true for their rational approximations, where p_{n}/q_{n} is the nth convergent of α. However, the question whether and when the symmetrization is really necessary remained wide open. We show that the L_{2} discrepancy of the nonsymmetrized lattice L_{n}(α) grows as in particular, characterizing the lattices for which the L_{2} discrepancy is optimal.

Original language | English (US) |
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Title of host publication | Recent Advances in Harmonic Analysis and Applications |

Subtitle of host publication | In Honor of Konstantin Oskolkov |

Publisher | Springer New York LLC |

Pages | 63-77 |

Number of pages | 15 |

ISBN (Print) | 9781461445647 |

DOIs | |

State | Published - 2013 |

Externally published | Yes |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 25 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Bibliographical note

Funding Information:The research of the authors is sponsored by NSF grants DMS 1101519, DMS 0906260, and EAR 0934747.

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