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Kannan
Kannan
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Let $K=\mathbb{Q}(\sqrt{d})$ be a real quadratic fields. S. Chowla conjectured that if $d=4m^2+1$ for $m \in \mathbb{Z}$ then there is exactly 6 real quadratic fields which has class number one. Hideo Yokoi proved this conjecture (almost!). Then the natural question arises: What can be said about similar real quadratic fields $\mathbb{Q}(\sqrt{a^2m^2+1})$ for $a \not = 4$$a \not = 2$ and $m$ a integers? I am looking for suitable reference for this question? Can someone suggest reference for this question?

Let $K=\mathbb{Q}(\sqrt{d})$ be a real quadratic fields. S. Chowla conjectured that if $d=4m^2+1$ for $m \in \mathbb{Z}$ then there is exactly 6 real quadratic fields which has class number one. Hideo Yokoi proved this conjecture (almost!). Then the natural question arises: What can be said about similar real quadratic fields $\mathbb{Q}(\sqrt{a^2m^2+1})$ for $a \not = 4$ and $m$ a integers? I am looking for suitable reference for this question? Can someone suggest reference for this question?

Let $K=\mathbb{Q}(\sqrt{d})$ be a real quadratic fields. S. Chowla conjectured that if $d=4m^2+1$ for $m \in \mathbb{Z}$ then there is exactly 6 real quadratic fields which has class number one. Hideo Yokoi proved this conjecture (almost!). Then the natural question arises: What can be said about similar real quadratic fields $\mathbb{Q}(\sqrt{a^2m^2+1})$ for $a \not = 2$ and $m$ a integers? I am looking for suitable reference for this question? Can someone suggest reference for this question?

Source Link
Kannan
Kannan
  • 19
  • 2

S. Chowla real quadratic fields

Let $K=\mathbb{Q}(\sqrt{d})$ be a real quadratic fields. S. Chowla conjectured that if $d=4m^2+1$ for $m \in \mathbb{Z}$ then there is exactly 6 real quadratic fields which has class number one. Hideo Yokoi proved this conjecture (almost!). Then the natural question arises: What can be said about similar real quadratic fields $\mathbb{Q}(\sqrt{a^2m^2+1})$ for $a \not = 4$ and $m$ a integers? I am looking for suitable reference for this question? Can someone suggest reference for this question?