Abstract
We construct some real quadratic fields whose class number is more than one from a class of sequences of positive integers. We also give a lower bound on the class number of such fields using Tatuzawa’s theorem and Yokoi invariant.
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F. Kawamoto, Y. Kishi, K. Tomita, Continued fraction expansions with even period and primary symmetric parts with extremely large end. Comm. Math. Univ. Sancti Pauli 64(2), 131–155 (2015)
F. Kawamoto, Y. Kishi, H. Suzuki, K. Tomita, Real quadratic fields, continued fractions, and a construction of primary symmetric parts of ELE type. Kyushu J. Math. 73(1), 165–187 (2019)
F. Kawamoto, K. Tomita, Continued fractions and certain real quadratic fields of minimal type. J. Math. Soc. Japan 60(3), 865–903 (2008)
S. Lang, Introduction to Diophantine Approximations (Addison-Wesley, Reading, MA, 1966)
O. Perron, Die Lehre von den KettenbrĂĽechen, Band I: Elementare KettenbrĂĽche, 3te Aufl. B. G. Teubner Verlagsgesellschaft, Stuttgart (1954)
T. Tatuzawa, On a theorem of Siegel. Jpn. J. Math. 21, 163–178 (1951)
H. Yokoi, New invariants and class number problem in real quadratic fields. Nagoya Math. J. 132, 175–197 (1993)
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Kawamoto, F., Kishi, Y. (2020). A Lower Bound for the Class Number of Certain Real Quadratic Fields. In: Chakraborty, K., Hoque, A., Pandey, P. (eds) Class Groups of Number Fields and Related Topics. Springer, Singapore. https://doi.org/10.1007/978-981-15-1514-9_4
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DOI: https://doi.org/10.1007/978-981-15-1514-9_4
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