dc.contributor.author | Banks, William David, 1964- | eng |

dc.contributor.author | Conflitti, Alessandro | eng |

dc.contributor.author | Friedlander, J. B. (John B.) | eng |

dc.contributor.author | Shparlinski, Igor E. | eng |

dc.date.issued | 2004 | eng |

dc.description | © Foundation Compositio Mathematica 2004. Cambridge Journals. doi: 10.1112/S0010437X03000022. | eng |

dc.description.abstract | We give estimates for exponential sums of the form Σn≤N Λ(n) exp(2πiagn/m), where m is a positive integer, a and g are integers relatively prime to m, and Λ is the von Mangoldt function. In particular, our results yield bounds for exponential sums of the form Σ p≤N exp(2πiaMp/m), where Mp is the Mersenne number; Mp = 2p −1 for any prime p.We also estimate some closely related sums, including
Σn≤N μ(n) exp(2πiagn/m) and Σn≤N μ2(n) exp(2πiagn/m), where μ is the Möbius function. | eng |

dc.identifier.citation | William D. Banks, Alessandro Conflitti, John B. Friedlander and Igor E. Shparlinski.Compositio Mathematica, vol. 140, issue 1 (2004), pp.15-30. | eng |

dc.identifier.uri | http://hdl.handle.net/10355/10638 | eng |

dc.relation.ispartof | Mathematics publications (MU) | eng |

dc.relation.ispartofcommunity | University of Missouri-Columbia. College of Arts and Sciences. Department of Mathematics | eng |

dc.source.uri | http://www.math.missouri.edu/~bbanks/papers/index.html | eng |

dc.subject | number theory | eng |

dc.subject.lcsh | Number theory | eng |

dc.title | Exponential Sums over Mersenne Numbers | eng |

dc.type | Article | eng |