Residuacity and genus theory of forms

Residuacity and genus theory of forms

We provide herein a simple, yet highly effective and efficient method for determining when a fundamental unit of negative norm of a real quadratic order is a quadratic residue modulo a given prime. We also provide criteria for the quartic residuacity of the fundamental unit determined by continued f...

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Bibliographic Details
Published in:Journal of number theory Vol. 132; no. 1; pp. 103 - 116
Main Authors: Mollin, Richard A., Srinivasan, Anitha
Format: Journal Article
Language:English
Published: Elsevier Inc 2012
Subjects:
Continued fractions
Pellʼs equation
Residuacity
secondary
Pellʼs equation
Residuacity
Continued fractions
primary
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Summary:We provide herein a simple, yet highly effective and efficient method for determining when a fundamental unit of negative norm of a real quadratic order is a quadratic residue modulo a given prime. We also provide criteria for the quartic residuacity of the fundamental unit determined by continued fraction expansions. The above yield known and new results as immediate consequences.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2011.06.003