A product related to the cubic Gauss sum
type: Item
instance of: scholarly article
title: A product related to the cubic Gauss sum
zbMATH Open document ID: 0599.10027
DOI: 10.1007/BF01057430
author: I. V. Reshetukha
published in: Ukrainian Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: One of the many ways of deriving the law of quadratic reciprocity and determining the sign of the quadratic Gaussian sum rests on properties of the product \(\prod_{1\leq r\leq (p-1)/2}2 \sin (2\pi r/p)\). The author here describes an analogous cubic product and shows how it leads to the law of cubic reciprocity. He also restates his conjecture [Mat. Zametki 7, 469-476 (1970; Zbl 0194.350)] of a link between this product and the argument of the cubic Gauss sum.
reviewed by: John H. Loxton
Mathematics Subject Classification ID: 11L03
Mathematics Subject Classification ID: 11A15
zbMATH DE Number: 3966195
zbMATH Keywords: Tikhonov's regularization method
zbMATH Keywords: law of cubic reciprocity
zbMATH Keywords: cubic Gauss sum
MaRDI profile type: Publication
cites work: Problem in the theory of cubic residues
cites work: Analytic determination of a certain product of cubic character
cites work: Q5798085
cites work: Q5542212
cites work: On Kummer Sums
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description: scientific article; zbMATH DE number 3966195