The sextic period polynomial
type: Item
instance of: scholarly article
title: The sextic period polynomial
zbMATH Open document ID: 0539.12003
author: D. H. Lehmer
author: E. T. Lehmer
published in: Pacific Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Let g be a primitive root of the prime \(p=ef+1\) and let \(\xi =\exp(2\pi i/p)\). The e periods \(\eta_ i\) are defined by \(\eta_ i=\sum^{f- 1}_{v=0}\xi^{g^{ev+i}}\quad(0\leq i\leq e-1).\) The period polynomial is the polynomial with roots \(\eta_ 0,\eta_ 1,...,\eta_{e-1}\). For \(e=6\) the authors give explicit expressions for the coefficients of the period polynomial, as well as its discriminant, in terms of the quadratic partitions \(4p=L^ 2+27M^ 2\) and \(p=A^ 2+3B^ 2.\) This paper fills a gap in the existing literature and should be useful to researchers in cyclotomy.
reviewed by: Kenneth S. Williams
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11T22
Mathematics Subject Classification ID: 11L03
Mathematics Subject Classification ID: 11R09
Mathematics Subject Classification ID: 11E16
Mathematics Subject Classification ID: 11D85
zbMATH DE Number: 3857237
zbMATH Keywords: cyclotomic numbers
zbMATH Keywords: period polynomial
zbMATH Keywords: cyclotomy
MaRDI profile type: Publication
full work available at URL: pjm.1984.111.341
OpenAlex ID: W2014857275
DOI: 10.2140/PJM.1984.111.341
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description: scientific article; zbMATH DE number 3857237