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2010 Rational residuacity of primes
Mark Budden, Alex Collins, Kristin Ellis Lea, Stephen Savioli
Involve 3(3): 249-257 (2010). DOI: 10.2140/involve.2010.3.249

Abstract

The most natural extensions to the law of quadratic reciprocity are the rational reciprocity laws, described using the rational residue symbol. In this article, we provide a reciprocity law from which many of the known rational reciprocity laws may be recovered by picking appropriate primitive elements for subfields of (ζp). As an example, a new generalization of Burde’s law is provided.

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Mark Budden. Alex Collins. Kristin Ellis Lea. Stephen Savioli. "Rational residuacity of primes." Involve 3 (3) 249 - 257, 2010. https://doi.org/10.2140/involve.2010.3.249

Information

Received: 27 April 2009; Accepted: 20 September 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1207.11008
MathSciNet: MR2739517
Digital Object Identifier: 10.2140/involve.2010.3.249

Subjects:
Primary: 11A15
Secondary: 11R18, 11R32

Rights: Copyright © 2010 Mathematical Sciences Publishers

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