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New bounds for fundamental units and class numbers of real quadratic fields

Sevcan Isikay|Ayten Pekin
대한수학회 (The Korean Mathematical Society)|2021.09|대한수학회보 (Bulletin of the KMS)|제58권 제5호|pp. 1149-1161|DOI 10.4134/BKMS.b200744

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참고문헌

키워드

Continued fractionclass numberfundamental unitreal quadratic field
주제분류수학

초록

In this paper, we present new bounds on the fundamental units of real quadratic fields $\mathbb{Q}(\sqrt{d})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.

Abstract

In this paper, we present new bounds on the fundamental units of real quadratic fields $\mathbb{Q}(\sqrt{d})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.

참고문헌 (17)

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