Bounds on trilinear and quadrilinear exponential sums
Number Theory
2017-02-10 v4 Classical Analysis and ODEs
Combinatorics
Abstract
We use an estimate of Aksoy Yazici, Murphy, Rudnev and Shkredov (2016) on the number of solutions of certain equations involving products and differences of sets in prime finite fields to give an explicit upper bound on trilinear exponential sums which improves the previous bound of Bourgain and Garaev (2009). We also obtain explicit bounds for quadrilinear exponential sums.
Keywords
Cite
@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}
}
Comments
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