Abstract
In this paper we discuss an analogue of Hilbert’s theorems 105 and 106, i.e. a reinterpretation of Gauss’ “genus theory”, for imaginary quadratic fields of class number one. We explicitly compute all biquadratic fields with Hasse unit index one whose ambiguous ideal classes over an imaginary quadratic field of class number one are principal.
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Acknowledgements
The authors would like to thank Dr. Maarefparvar and Dr. Shahoseini for very helpful discussions that significantly improved the exposition of this paper. We also thank the anonymous referee for a very careful reading of the manuscript and for making helpful suggestions.
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A. Rajaei’s research was supported by Grant 1401110121 from IPM.
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Naroui, R., Rajaei, A. On quadratic Ostrowski extensions of imaginary quadratic fields. Ramanujan J 62, 967–982 (2023). https://doi.org/10.1007/s11139-023-00726-0
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DOI: https://doi.org/10.1007/s11139-023-00726-0