CONGRUENT NUMBERS AND LOWER BOUNDS ON CLASS NUMBERS OF REAL QUADRATIC FIELDS

Jigu Kim; Yoonjin Lee

doi:10.1090/proc/15993

CONGRUENT NUMBERS AND LOWER BOUNDS ON CLASS NUMBERS OF REAL QUADRATIC FIELDS

Jigu Kim, Yoonjin Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	4671-4684
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	11
DOIs	https://doi.org/10.1090/proc/15993
State	Published - 1 Nov 2022

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© 2022 American Mathematical Society. All rights reserved.

Keywords

Class numbers
elliptic curves

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10.1090/proc/15993

Cite this

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CONGRUENT NUMBERS AND LOWER BOUNDS ON CLASS NUMBERS OF REAL QUADRATIC FIELDS

Abstract

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Keywords

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