Congruent numbers and lower bounds on class numbers of real quadratic fields

We give effective lower bounds on caliber numbers of the parametric family of real quadratic fields \mathbb {Q}(\sqrt {t^4-n^2}) as t varies over positive integers for a congruent number n. Furthermore, we provide lower bounds on class numbers of Richaud-Degert type real quadratic fields of the form...

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Veröffentlicht in:	Proceedings of the American Mathematical Society 2022-11, Vol.150 (11), p.4671-4684
Hauptverfasser:	Kim, Jigu, Lee, Yoonjin
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Sprache:	eng
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description	We give effective lower bounds on caliber numbers of the parametric family of real quadratic fields \mathbb {Q}(\sqrt {t^4-n^2}) as t varies over positive integers for a congruent number n. Furthermore, we provide lower bounds on class numbers of Richaud-Degert type real quadratic fields of the form \mathbb {Q}(\sqrt {n^2k^4-1}) for positive integers k and congruent numbers n whose elliptic curves have algebraic rank greater than 2.
doi_str_mv	10.1090/proc/15993
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title	Congruent numbers and lower bounds on class numbers of real quadratic fields
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