白文,任剛練

(1.西北大學數(shù)學系,陜西西安 710069;2.咸陽師范學院數(shù)學與信息科學學院,陜西咸陽 712000)

關于廣義齊性Cochrane和的加權均值

白文1,任剛練2

(1.西北大學數(shù)學系,陜西西安 710069;2.咸陽師范學院數(shù)學與信息科學學院,陜西咸陽 712000)

研究了廣義齊性Cochrane和的一些加權均值,并利用不完全區(qū)間上特征和的性質(zhì),Dirichlet函數(shù)的均值估計以及周期Bernoulli多項式的性質(zhì),得到一些較強的漸近公式.

廣義齊性Cochrane和;周期Bernoulli多項式;Dirichlet L-函數(shù);特征和

1 引言及定理

2000年,Todd Cochrane引入下面的和式[1]:

十分類似,許多作者對它作了深入研究并獲得許多優(yōu)美的結果.

2 幾個引理

為了完成定理的證明,需要以下幾個引理:

引理1令m為任意給定常數(shù),n為非負整數(shù),p為素數(shù).對于模p的任意奇特征χ,即χ(-1)=-1,則有

3 定理的證明

現(xiàn)在來完成定理的證明.

根據(jù)引理2,引理4可得

這樣就完成定理2的證明.由(24)式和(25)式可得出推論.

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On the weighted mean of generalized homogeneous Cochrane sum

Bai Wen1,Ren Ganglian2
(1.Department of Mathematics,Northwest University,Xi′an710069,China; 2.College of Mathematics and Information Science,Xianyang Normal University,Xianyang712000,China)

The weighted mean of generalized homogeneous Cochrane sum is studied.By using the properties of character sum over the incomplete intervals,mean value estimate of Dirichlet L-functions,and the periodic Bernoulli polynomial,some related asymptotic formulas are obtained.

generalized homogeneous Cochrane sum,periodic Bernoulli polynomial,L-functions, character sum

O156.2

A

1008-5513(2013)02-0190-07

10.3969/j.issn.1008-5513.2013.02.013

2012-12-10.

國家自然科學基金(2009JQ1009);陜西省教育廳自然科學專項基金(09JK803).

白文(1986-),碩士生,研究方向：數(shù)論.

2010 MSC:11N05