Heath-Brown, D. R. (2000) *Kummer's conjecture for cubic Gauss sums.* Israel Journal of Mathematics, 120 . pp. 97-124.

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## Abstract

Let where is the normalized cubic Gauss sum for an integer of the field . It is shown that , for every and any . This improves on the estimate established by Heath-Brown and Patterson in demonstrating the uniform distribution of the cubic Gauss sums around the unit circle. When it is conjectured that the above sum is asymptotically of order , so that the upper bound is essentially best possible. The proof uses a cubic analogue of the author's mean value estimate for quadratic character sums.

Item Type: | Article |
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Subjects: | H - N > Number theory |

Research Groups: | Number Theory Group |

ID Code: | 158 |

Deposited By: | Roger Heath-Brown |

Deposited On: | 14 Jan 2005 |

Last Modified: | 20 Jul 2009 14:19 |

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