关于完全三角和估计的华罗庚方法

完全有理三角和就是如下形式的和式 Ｓ（ψ，ｑ）＝Σ＾ｑｘ＝１ｅｑ（ψ（ｘ））， 其中ψ（ｘ）是整系数的多项式。许多作者得到了关于Ｓ（ψ，ｑ）的估计的结果。本文发展了华罗庚方法并研究了如下形式的完全有理三角和 Ｓ（Ｒ，ｑ）＝Σ＾ｑｘ＝１ｅｑ（Ｒ（ｘ）），

On a Method of Hua Loo-Keng of Estimating Complete Trigononomtric Sums

Complete rational trigonometric sum is a sum of the form where is a poIynomial with integral coefficients,many results for the estimations of S were obtained by many authors.In this paper the author develops the Hua's method and studies the complete rational trigonometric sums where R(x)is a rational function,some new results for the upper bound of S( R ,q)are obtained.