## Abstract

We determine the exact shape of the G_{2} equidistribution law for the one parameter family of exponential sums over F_{p} ^{×}, ∑ x mod p, x≠0 χ_{2}(x) exp(2πi(x^{7}+tx)/p). Here χ_{2}(x) denotes the quadratic character (x/p), t in F_{p}, is the parameter, and p is any prime other than 2 or 7. This answers a question raised in Keating et al. (J. Phys. A Math. Gen. 36 (2003) 2943, footnote 3) and in Serre (pers. commun., March 7, 2002). We also analyze the analogous families when 7 is replaced by any odd integer n≥3.

Original language | English (US) |
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Pages (from-to) | 221-269 |

Number of pages | 49 |

Journal | Finite Fields and their Applications |

Volume | 10 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2004 |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Algebra and Number Theory
- Engineering(all)
- Applied Mathematics

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