A mean value of Cochrane sum

被引:0
作者
Zhe Feng Xu
机构
[1] Xi’an Jiaotong University,College of Science
[2] Northwest University,Department of Mathematics
来源
Acta Mathematica Sinica, English Series | 2009年 / 25卷
关键词
Dedekind sum; Cochrane sums; mean value; asymptotic formula; 11F20; 11L26;
D O I
暂无
中图分类号
学科分类号
摘要
Let q > 4 be an integer. The main purpose of this paper is to study the mean value of Cochrane sum C(a, q) in quarter intervals, and obtain a sharp asymptotic formula for it.
引用
收藏
页码:223 / 234
页数:11
相关论文
共 18 条
[1]  
Carlitz L.(1953)The reciprocity theorem of Dedekind sums Pacific J. Math. 3 513-522
[2]  
Rademacher H.(1955)On the transformation of log J. Indian. Math. Soc. 19 25-30
[3]  
Conrey J. B.(1982)( J. Number Theory 41 27-31
[4]  
Fransen E.(2000)) Acta Math. Hungar. 86 275-289
[5]  
Klein R.(2002)Mean values of Dedekind sums International J. of Math. and Math. Sci. 32 47-55
[6]  
Scott C.(2002)A note on the mean square valueof the Dedekind sums J. Math. Anal. Appl. 267 89-96
[7]  
Zhang W. P.(2003)On a sum analogous to Dedekind sum and its mean square value formula J. Math. Anal. Appl. 288 646-659
[8]  
Zhang W. P.(2006)On a Cochrane sum and its hybrid mean value formula J. Number Theory 117 131-145
[9]  
Zhang W. P.(1990)A note on the Cochrane sum and its hybrid mean value formula Acta Arith. 55 59-73
[10]  
Zhang W. P.(1996)On the order of the high-dimensional Cochrane sum and its mean value Journal de Theorie des Nombres 8 429-442