A note on the hyper Cochrane sum
type: Item
instance of: scholarly article
title: A note on the hyper Cochrane sum
zbMATH Open document ID: 1297.11024
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2013-08-09T00:00:00Z
review text: Let \(q\) and \(h\) be integers with \(q\geq 3\) and \((h,q)=1\). Let \(\mathbf{m}=\left(m_1,\cdots,m_k,m_{k+1}\right)\in \mathbb{Z}^{k+1}\). The hyper Cochrane sum is defined as following: \[ C\left(h,q;\mathbf{m},k\right)=\mathop{\sum_{a_1=1}^{q}}_{(a_1,q)=1}\cdots \mathop{\sum_{a_k=1}^{q}}_{(a_k,q)=1}\overline{B}_{m_1}\left(\frac{a_1}{q}\right)\cdots \overline{B}_{m_k}\left(\frac{a_k}{q}\right)\overline{B}_{m_{k+1}}\left(\frac{h\overline{a_1\cdots a_k}}{q}\right), \] where \(\overline{B}_{n}(x)\) is the \(n\)-th Bernoulli periodic function, \(\overline{y}\) is the multiplicative inverse of \(y\) modulo \(q\). This paper provides some upper bounds for \(C\left(h,q;\mathbf{m},k\right)\).
Mathematics Subject Classification ID: 11F20
Mathematics Subject Classification ID: 11L05
zbMATH DE Number: 6197287
zbMATH Keywords: Dedekind sum
zbMATH Keywords: hyper Cochrane sum
zbMATH Keywords: upper bound
author: Tianping Zhang
MaRDI profile type: Publication
full work available at URL: s13226-013-0015-x
OpenAlex ID: W1987548457
cites work: Q4101884
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cites work: Q4778329
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DOI: 10.1007/S13226-013-0015-X
description: scientific article; zbMATH DE number 6197287