三线性与四线性指数和的界
数论
2017-02-10 v4 经典分析与常微分方程
组合数学
摘要
我们利用Aksoy Yazici、Murphy、Rudnev和Shkredov (2016)关于素有限域中涉及集合乘积与差的方程解数的估计，给出了三线性指数和的一个显式上界，改进了Bourgain与Garaev (2009)先前的界。我们也获得了四线性指数和的显式界。
引用
@article{arxiv.1604.08469,
title = {Bounds on trilinear and quadrilinear exponential sums},
author = {Giorgis Petridis and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:1604.08469},
year = {2017}
}
备注
31 pages. Accepted in Journal d'Analyse Mathematique. The introduction, bibliography and Section 2.1 have been extended to include a historical overview and ancestry of the results presented in this paper. Theorem 1.9, a further application of the exponential sums bounds, was added in Section 1.4 and proved in Section 4.4. We report recent progress in Section 1.5