Geodesic
On the class number of the maximal real subfields of a family of cyclotomic fields
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 937-940
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For any square-free positive integer $m\equiv {10}\pmod {16}$ with $m\geq 26$, we prove that the class number of the real cyclotomic field $\mathbb {Q}(\zeta _{4m}+\zeta _{4m}^{-1})$ is greater than $1$, where $\zeta _{4m}$ is a primitive $4m$th root of unity.
For any square-free positive integer $m\equiv {10}\pmod {16}$ with $m\geq 26$, we prove that the class number of the real cyclotomic field $\mathbb {Q}(\zeta _{4m}+\zeta _{4m}^{-1})$ is greater than $1$, where $\zeta _{4m}$ is a primitive $4m$th root of unity.
DOI : 10.21136/CMJ.2023.0364-22
Classification : 11R11, 11R18, 11R29
Keywords: maximal real subfield of cyclotomic field; real quadratic field; class number 
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Ram, Mahesh Kumar. On the class number of the maximal real subfields of a family of cyclotomic fields. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 937-940. doi: 10.21136/CMJ.2023.0364-22

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