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## Prime power exponential and character sums with explicit evaluations

Doctor of Philosophy / Department of Mathematics / Christopher Pinner / Exponential and character sums occur frequently in number theory. In most applications

one is only interested in estimating such sums. Explicit evaluations of such sums are rare.

In this thesis we succeed in evaluating three types of sums when p is a prime and

m is sufficiently large. The twisted monomial sum, the binomial character sum,

and the generalized Jacobi sum.

We additionally show that these are all sums which can be expressed in terms of classical Gauss sums.

Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/18277 |

Date | January 1900 |

Creators | Pigno, Vincent |

Publisher | Kansas State University |

Source Sets | K-State Research Exchange |

Language | en_US |

Detected Language | English |

Type | Dissertation |

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