Osaka Journal of Mathematics

Continued fractions with even period and an infinite family of real quadratic fields of minimal type

Fuminori Kawamoto and Koshi Tomita

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Abstract

In a previous paper [4], we introduced the notion of real quadratic fields with period $l$ of minimal type in terms of continued fractions. As a consequence, we have to examine a construction of real quadratic fields with period $\ge 5$ of minimal type in order to find many real quadratic fields of class number 1. When $l \ge 4$, it appears that there exist infinitely many real quadratic fields with period $l$ of minimal type. Indeed, we provided an infinitude of real quadratic fields with period 4 of minimal type in [4]. In this paper, we construct an infinite family of real quadratic fields with large even period of minimal type whose class number is greater than any given positive integer, and whose Yokoi invariant is greater than any given positive integer.

Article information

Source
Osaka J. Math., Volume 46, Number 4 (2009), 949-993.

Dates
First available in Project Euclid: 15 December 2009

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1260892836

Mathematical Reviews number (MathSciNet)
MR2604917

Zentralblatt MATH identifier
1247.11140

Subjects
Primary: 11R29: Class numbers, class groups, discriminants
Secondary: 11A55: Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15] 11R11: Quadratic extensions 11R27: Units and factorization

Citation

Kawamoto, Fuminori; Tomita, Koshi. Continued fractions with even period and an infinite family of real quadratic fields of minimal type. Osaka J. Math. 46 (2009), no. 4, 949--993. https://projecteuclid.org/euclid.ojm/1260892836


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