Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

HOME ALL ARTICLES View

J. Korean Math. Soc. 2007; 44(6): 1243-1254

Printed November 1, 2007

Copyright © The Korean Mathematical Society.

On the mean values of the homogeneous Dedekind sums and Cochrane sums in short intervals

Huaning Liu

Northwest University

Abstract

In this paper, we study the mean values of the homogeneous Dedekind sums and Cochrane sums in short intervals $\left[1, \frac{p}{3}\right]$ and $\left[1, \frac{p}{4}\right]$, and give some asymptotic formulae by using the mean values of the Dirichlet $L$-functions.

Keywords: Dedekind sums, Cochrane sums, homogeneous, mean values

MSC numbers: 11F20