CONGRUENT NUMBERS AND LOWER BOUNDS ON CLASS NUMBERS OF REAL QUADRATIC FIELDS
- 주제(기타) Mathematics, Applied; Mathematics
- 설명문(일반) [Kim, Jigu] Ewha Womans Univ, Inst Math Sci, 52 Ewhayeodae Gil, Seoul 03760, South Korea; [Lee, Yoonjin] Ewha Womans Univ, Dept Math, 52 Ewhayeodae Gil, Seoul 03760, South Korea; [Lee, Yoonjin] Korea Inst Adv Study, 85 Hoegi Ro, Seoul 02455, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 AMER MATHEMATICAL SOC
- 발행년도 2022
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000203034
- 본문언어 영어
- Published As https://doi.org/10.1090/proc/15993
초록/요약
We give effective lower bounds on caliber numbers of the parametric family of real quadratic fields Q(root 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 Q(root n(2)k(4) - 1) for positive integers k and congruent numbers n whose elliptic curves have algebraic rank greater than 2.
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