An improved Mordell type bound for exponential sums期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

An improved Mordell type bound for exponential sums

Authors:	Todd Cochrane Christopher Pinner

Affiliation:	Department of Mathematics, Kansas State University, Manhattan, Kansas 66506 ; Department of Mathematics, Kansas State University, Manhattan, Kansas 66506

Abstract:	For a sparse polynomial $f(x)=sum_{i=1}^r a_ix^{k_i}in mathbb Z [x]$ , with and , we show that $begin{displaymath}leftvertsum_{x=1}^{p-1} e^{2pi i f(x)/p} rightvert leq... ...rac{2}{r}} (k_1cdots k_r)^{frac{1}{r^2}}p^{1-frac{1}{2r}}, end{displaymath}$ thus improving upon a bound of Mordell. Analogous results are obtained for Laurent polynomials and for mixed exponential sums.

Keywords:	Exponential sums

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