Besser, A.; Moree, P. On an invariant related to a linear inequality. (English) Zbl 1015.15012 Arch. Math. 79, No. 6, 463-471 (2002). For a sequence \((\alpha_1 ,\alpha_2, \ldots ,\alpha_m)\in \mathbb{R}^m\) and given \(1\leq i<j\leq m\) the authors consider a signed count of all solutions of \[ |\alpha_i -\alpha_j |< \sum \varepsilon_k \alpha_k < \alpha_i+\alpha_j \] where \(\varepsilon_i=\varepsilon_j=0\) and all other \(\varepsilon =\pm 1\). For \(m\) odd 3 proofs are given that this signed count is independent of the choice of \(i,j\). Several related results are proved and this invariant is related to Rademacher functions. Reviewer: Ki Hang Kim (Montgomery) Cited in 1 Review MSC: 15A39 Linear inequalities of matrices 11B83 Special sequences and polynomials Keywords:Rademacher function; trigonometric integral; linear inequality PDFBibTeX XMLCite \textit{A. Besser} and \textit{P. Moree}, Arch. Math. 79, No. 6, 463--471 (2002; Zbl 1015.15012) Full Text: DOI arXiv Online Encyclopedia of Integer Sequences: An invariant of the set {Log(2), Log(3), Log(5),..., Log(Prime(2n)), Log(Prime(2n+1))}. References: [1] I. S. Gradshteyn andI. M. Ryzhik, Table of integrals, series, and products. New York 1980. · Zbl 0521.33001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.