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arxiv: 1812.02488 · v3 · pith:EQVQF7SZnew · submitted 2018-12-06 · 🧮 math.NT

A note on certain real quadratic fields with class number upto three

Kalyan Chakraborty , Azizul Hoque , Mohit Mishra This is my paper
classification 🧮 math.NT
keywords fieldsclassnumberquadraticrealcertaincriteriaobtain
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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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  1. Lower bound for class number of certain real quadratic fields

    math.NT 2019-06 unverdicted novelty 5.0

    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.