Continued fractions and real quadratic fields
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Publication:1106884
DOI10.1016/0022-314X(88)90015-7zbMath0652.12002OpenAlexW2012847825MaRDI QIDQ1106884
Publication date: 1988
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0022-314x(88)90015-7
Related Items (24)
Fundamental units for real quadratic fields determined by continued fraction conditions ⋮ Bounds of the ideal class numbers of real quadratic function fields ⋮ Unnamed Item ⋮ ON CLASS NUMBER ONE FOR THE REAL QUADRATIC FIELD ⋮ On some properties of partial quotients of the continued fraction expansion of \(\sqrt{d}\) with even period ⋮ Use of the rabinowitsch polynomial to determine the class groups of a real quadratic field ⋮ Fields of small class number in the family \(\mathbb{Q}(\sqrt{9m^2+4m})\) ⋮ A handy technique for fundamental unit in specific type of real quadratic fields ⋮ Quadratische Ordnungen mit großer Klassenzahl. (Quadratic orders with large class number) ⋮ Continued fractions and Gauss class number problem for real quadratic fields ⋮ Class number one problem for the real quadratic fields \(\mathbb{Q}(\sqrt{m^2+2r})\) ⋮ The non-normal quartic CM-fields and the octic dihedral CM-fields with relative class number two ⋮ On the Continued Fraction Expansions of $$\sqrt{p}$$ and $$\sqrt{2p}$$ for Primes $$p\equiv 3\pmod 4$$ ⋮ On the divisor function and class numbers of real quadratic fields. III ⋮ The class number one problem for some non-abelian normal CM-fields ⋮ Continued fractions and certain real quadratic fields of minimal type ⋮ Relative norm of the fundamental unit of certain biquadratic fields and parity of the lengths of cycles of reduced ideals ⋮ On fundamental units of real quadratic fields of class number 1 ⋮ The fundamental unit and bounds for class numbers of real quadratic fields ⋮ On determining certain real quadratic fields with class number one and relating this property to continued fractions and primality properties ⋮ Quadratic extensions of the rational field, the Gauss field or the field of cubic roots of unity of caliber 1 ⋮ Distribution of Class Numbers in Continued Fraction Families of Real Quadratic Fields ⋮ Orders in quadratic fields. I ⋮ Class number problem for a family of real quadratic fields
Cites Work
- Class number one criteria for real quadratic fields. I
- A characterization of certain real quadratic fields
- Über Pell'sche Gleichungen und Kettenbrüche. (On Pell equations and continued fractions)
- Real quadratic number fields with large fundamental units
- Lower Bounds for Class Numbers of Real Quadratic Fields
- On a criterion for the class number of a quadratic number field to be one
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