The class number one problem for the real quadratic fields $\mathbb {Q}(\sqrt {(an)^2+4a})$
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Publication:2787077
DOI10.4064/aa7957-12-2015zbMath1358.11119arXiv1508.05644OpenAlexW2308311019MaRDI QIDQ2787077
Kostadinka Lapkova, András Biró
Publication date: 24 February 2016
Published in: Acta Arithmetica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1508.05644
Quadratic extensions (11R11) Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42)
Related Items (12)
Class numbers of certain families of totally real biquadratic fields and a result of Mollin ⋮ NECESSARY AND SUFFICIENT CONDITIONS FOR UNIQUE FACTORIZATION IN ℤ[(-1 + √<i>d</i>)/2] ⋮ Prime producing quadratic polynomials associated with real quadratic fields of class-number one ⋮ Fields of small class number in the family \(\mathbb{Q}(\sqrt{9m^2+4m})\) ⋮ Unnamed Item ⋮ Some criteria for class numbers to be non-one ⋮ On the \(k\)-free values of the polynomial \(xy^k + C\) ⋮ On fundamental units of real quadratic fields of class number 1 ⋮ On the structure of order 4 class groups of \(\mathbb{Q}(\sqrt{n^2+1})\) ⋮ Distribution of Class Numbers in Continued Fraction Families of Real Quadratic Fields ⋮ A necessary and sufficient condition for \(k=\mathbb{Q}\left ( \sqrt{4 n^2 + 1}\right)\) to have class number \(\omega\left( n\right)+c \) ⋮ Lower bound for class numbers of certain real quadratic fields
Uses Software
Cites Work
- Unnamed Item
- Zeta functions for ideal classes in real quadratic fields, at \(s=0\)
- Class number one problem for real quadratic fields of a certain type
- On some problems of the arithmetical theory of continued fractions
- Mollin's conjecture
- The complete determination of wide Richaud–Degert types which are not 5 modulo 8 with class number one
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