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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2021.9
- 수록면
- 613 - 617 (5page)
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For a positive square-free integer $m$, let $K=\mathbb{Q}(\sqrt{m})$ be a real quadratic field. The relative class number $H_d(f)$ of $K$ of discriminant $d$is the ratio of class numbers $\mathcal{O}_K$ and $\mathcal{O}_f$, where $\mathcal{O}_K$ is the ring of integers of $K$ and $\mathcal{O}_f$is the order of conductor $f$ given by $\mathbb{Z}+f\mathcal{O}_K$. In 1856, Dirichlet showed that for certain $m$ there exists an infinite number of $f$ such thatthe relative class number $H_d(f)$ is one. But it remained open as to whether there exists such an $f$ for each $m$. In this paper, we give a result forexistence of real quadratic field $\mathbb{Q}(\sqrt{m})$ with relative class number one where the period of continued fraction expansion of $\sqrt{m}$ is $6$.
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참고문헌 (17)
참고문헌 신청
N. C. Ankeny / 1952 / The class-number of real quaratic fields / Ann. of Math. (2) 56:479~493
변동호 / 2012 / A NOTE ON UNITS OF REAL QUADRATIC FIELDS / 대한수학회보 49(4):767~774
B. D. Beach / 1971 / Some computer results on units in qua-dratic and cubic fields / Proc. 25th Summer Meeting Can. Math. Congress :609~648
H. Cohn / 1962 / A second course in number theory / Wiley
H. Cohn / 1962 / A numerical study of the relative class numbers of real quadratic integral do-mains / Math. Comp 16:127~140
변동호 / 2012 / A NOTE ON UNITS OF REAL QUADRATIC FIELDS / 대한수학회보 49(4):767~774
B. D. Beach / 1971 / Some computer results on units in qua-dratic and cubic fields / Proc. 25th Summer Meeting Can. Math. Congress :609~648
H. Cohn / 1962 / A second course in number theory / Wiley
H. Cohn / 1962 / A numerical study of the relative class numbers of real quadratic integral do-mains / Math. Comp 16:127~140
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