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Keywords:
maximal real subfield of cyclotomic field; real quadratic field; class number
maximal real subfield of cyclotomic field; real quadratic field; class number
Summary:
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.
References:
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