A mean value of Cochrane sum
type: Item
instance of: scholarly article
title: A mean value of Cochrane sum
zbMATH Open document ID: 1215.11078
author: Zhefeng Xu
publication date: 2009-11-11T00:00:00Z
review text: Let \(q\) be a positive integer. For an integer \(a\) relatively prime to \(q\), let \(\overline a\) denote the multiplicative inverse of \(a\) modulo \(q\). Then one can define the so-called Cochrane sum \(C(h,q)\) by \[ C(h,q)=\sum_{{a=1}\atop{(a,q)=1}}^q\left(\left(\frac aq\right)\right)\left(\left(\frac{\overline{ a}h}q\right)\right) \] for arbitrary integers \(h\), where for a real number \(x\), we let \(((x))=x-\lfloor x\rfloor-1/2\) if \(x\) is not an integer and \(((x))=0\) if \(x\) is an integer. The purpose of the paper under review is to obtain an asymptotic formula for the sum \(\sum_{a<q/4}\sum_{b<q/4}C(ab,q)\).
Mathematics Subject Classification ID: 11L26
Mathematics Subject Classification ID: 11F20
zbMATH DE Number: 5629495
zbMATH Keywords: Dedekind sum
zbMATH Keywords: Cochrane sums
reviewed by: Yifan Yang
MaRDI profile type: Publication
full work available at URL: s10114-008-7188-y
OpenAlex ID: W2113867969
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DOI: 10.1007/S10114-008-7188-Y
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5629495