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Rational
residuacity of primes
Mark Budden, Alex Collins, Kristin Ellis Lea and Stephen Savioli
Vol. 3 (2010), No. 3, 249–257
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Abstract |
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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 . As an example, a new generalization of Burde’s law is provided. |
Keywords
reciprocity laws, ramification of prime ideals, cyclotomic
fields
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Mathematical Subject Classification 2000
Primary: 11A15
Secondary: 11R32, 11R18
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Milestones
Received: 27 April 2009
Accepted: 20 September 2010
Published: 16 October 2010
Proposed: Filip Saidak
Communicated by Filip Saidak
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Authors |
| Mark Budden | |
| Department of Mathematics and
Computer Science Western Carolina University Cullowhee, NC 28723 United States |
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| Alex Collins | |
| Department of Mathematics Armstrong Atlantic State University 11935 Abercorn St. Savannah, GA 31419 United States |
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| Kristin Ellis Lea | |
| Department of Mathematics Armstrong Atlantic State University 11935 Abercorn St. Savannah, GA 31419 United States |
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| Stephen Savioli | |
| Department of Mathematics Armstrong Atlantic State University 11935 Abercorn St. Savannah, GA 31419 United States |
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