@article{39d94d91a8a84526882b5ae89ddc2578,
title = "CONGRUENT NUMBERS AND LOWER BOUNDS ON CLASS NUMBERS OF REAL QUADRATIC FIELDS",
abstract = "We give effective lower bounds on caliber numbers of the parametric family of real quadratic fields Q(√t4 − n2) 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(√n2k4 − 1) for positive integers k and congruent numbers n whose elliptic curves have algebraic rank greater than 2.",
keywords = "Class numbers, elliptic curves",
author = "Jigu Kim and Yoonjin Lee",
note = "Funding Information: The authors were supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2019R1A6A1A11051177). The first author was also supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2020R1I1A1A01074746), and the second author was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST)(NRF-2022R1A2C1003203). Publisher Copyright: {\textcopyright} 2022 American Mathematical Society. All rights reserved.",
year = "2022",
month = nov,
day = "1",
doi = "10.1090/proc/15993",
language = "English",
volume = "150",
pages = "4671--4684",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "11",
}