Heath-Brown, D. R. (2000) Kummer's conjecture for cubic Gauss sums. Israel Journal of Mathematics, 120 . pp. 97-124.
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.
|Subjects:||H - N > Number theory|
|Research Groups:||Number Theory Group|
|Deposited By:||Roger Heath-Brown|
|Deposited On:||14 Jan 2005|
|Last Modified:||20 Jul 2009 14:19|
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