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PreprintCC BY 4.0arXiv

On the class number of real multiquadratic fields

  • Mohamed Mahmoud Chems-Eddin
  • Hamza El Mamry
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Abstract

In their 1988 monograph, Conner and Hurrelbrink classified all real quadratic and biquadratic fields with odd class number. They also investigated real quadratic fields whose $2$-class numbers are equal to $2$. Their results, together with some well-known results of Ku{č}era, provide a complete classification of real quadratic number fields with $2$-class number $2$. The main aim of this paper is to provide a complete classification of all real biquadratic fields whose $2$-class numbers equal $2$; and moreover, we draw the complete list all real multiquadratic fields with odd class numbers. Finally, as an appendix we give explicit formulas for √(εd), where εd denotes the fundamental unit of the real quadratic field ℚ(√d).

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Cite

BibTeXRIS
BibTeX
@misc{chemseddin2026class,
  title = {{On the class number of real multiquadratic fields}},
  author = {Mohamed Mahmoud Chems-Eddin and Hamza El Mamry},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07180},
  eprint = {2610.07180},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07180},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the class number of real multiquadratic fields
AU  - Mohamed Mahmoud Chems-Eddin
AU  - Hamza El Mamry
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.07180
UR  - https://arxiv.org/abs/2610.07180
AB  - In their 1988 monograph, Conner and Hurrelbrink classified all real quadratic and biquadratic fields with odd class number. They also investigated real quadratic fields whose $2$-class numbers are equal to $2$. Their results, together with some well-known results of Ku{č}era, provide a complete classification of real quadratic number fields with $2$-class number $2$. The main aim of this paper is to provide a complete classification of all real biquadratic fields whose $2$-class numbers equal $2$; and moreover, we draw the complete list all real multiquadratic fields with odd class numbers. Finally, as an appendix we give explicit formulas for √(ε_d), where ε_d denotes the fundamental unit of the real quadratic field ℚ(√d).
ER  -