HeathBrown, D. R. (2000) Kummer's conjecture for cubic Gauss sums. Israel Journal of Mathematics, 120 . pp. 97124.

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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 HeathBrown 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 

Subjects:  H  N > Number theory 
Research Groups:  Number Theory Group 
ID Code:  158 
Deposited By:  Roger HeathBrown 
Deposited On:  14 Jan 2005 
Last Modified:  29 May 2015 18:17 
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