Necessary and sufficient conditions for the central norm to equal 2h in the simple continued fraction expansion of sqrt(2hc) for any odd c > 1

• Autores: R. A. Mollin
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 48, Nº 1, 2005, págs. 121-132
• Idioma: inglés
• DOI: 10.4153/cmb-2005-011-0
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• Resumen

  • We look at the simple continued fraction expansion of sqrt{D} for any D = 2hc where c > 1 is odd with a goal of determining necessary and sufficient conditions for the central norm (as determined by the infrastructure of the underlying real quadratic order therein) to be 2h. At the end of the paper, we also address the case where D = c is odd and the central norm of sqrt{D} is equal to 2.