On Maillet determinant
type: Item
instance of: scholarly article
title: On Maillet determinant
zbMATH Open document ID: 0535.12004
DOI: 10.1016/0022-314X(84)90064-7
author: Kai Wang
published in: Journal of Number Theory
publication date: 1984-01-01T00:00:00Z
review text: For an integer \(m>2\), Maillet's determinant is defined as \(D_ m=\det(R(ab'))\), \(1\leq a,b<m/2\), \((ab,m)=1\), where \(bb'\equiv 1\pmod m\) and \(R(k)\) denotes the least positive residue mod \(m\) of \(k\). The author computes \(D_ m\) in terms of certain character sums closely connected to the relative class number of the \(m\)-th cyclotomic field. Essentially the same result was obtained recently by \textit{K. Tateyama} [Sci. Pap. Coll. Gen. Educ., Univ. Tokyo 32, 97--100 (1982; Zbl 0508.12006)].
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11L10
Mathematics Subject Classification ID: 11C20
zbMATH DE Number: 3849357
zbMATH Keywords: Maillet determinant
zbMATH Keywords: character sums
zbMATH Keywords: relative class number of the m-th cyclotomic field
MaRDI profile type: Publication
cites work: Q5521595
cites work: Maillet’s determinant
cites work: The nonexistence of nontrivial linear relations between the roots of a certain irreducible equation
cites work: Number fields
cites work: On a theorem of S. Chowla
description: scientific article; zbMATH DE number 3849357