Kummer's conjecture for cubic Gauss sums

Journal article

It is shown that the normalized cubic Gauss sums for integers c = 1 ((mod 3)) of the field Q root -3 satisfy[GRAPHICS]for every I E Z and any E > 0. This improves on the estimate established by Heath-Brown and Patterson [4] in demonstrating the uniform distribution of the cubic Gauss sums around the unit circle. When l = 0 it is conjectured that the above sum is asymptotically of order X-5/6, 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 [3].

Authors: Heath-Brown, D

• Publication status: Published
• Journal: ISRAEL JOURNAL OF MATHEMATICS
• Volume: 120
• Pages: 97-124
• Publication date: 2000-01-01
• EISSN: 1565-8511
• ISSN: 0021-2172
• Language: English