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.
A note on certain real quadratic fields with class number upto three
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abstract
We obtain criteria for the class number of certain Richaud-Degert type real quadratic fields to be 3. We also treat a couple of families of real quadratic fields of Richaud-Degert type that were not considered earlier, and obtain similar criteria for the class number of such fields to be 2 and 3.
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2019 1verdicts
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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.