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On the structure of order 4 class groups of mathbb{Q}(sqrt{n²+1})
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On the structure of order 4 class groups of mathbb{Q}(sqrt{n²+1})
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Groups of order $4$ are isomorphic to either $\mathbb{Z}/4\mathbb{Z}$ or $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$. We give certain sufficient conditions permitting to specify the structure of class groups of order $4$ in the family of real quadratic fields $\mathbb{Q}{(\sqrt{n^2+1})}$ as $n$ varies over positive integers. Further, we compute the values of Dedekind zeta function attached to these quadratic fields at the point $-1$. As a side result, we show that the size of the class group of this family could be made as large as possible by increasing the size of the number of distinct odd prime factors of $n$.
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Cited by 1 Pith paper
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Lower bound for class number of certain real quadratic fields
Explicit lower bounds for h(n²+r) (r=1,4) are derived together with zeta-function criteria that reduce the families in Chowla and Yokoi conjectures and give cyclicity conditions for prime-power class groups.
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