Journal of the Ramanujan Mathematical Society

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Divisibility of Class Numbers of Certain Families of Quadratic Fields


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1 Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211 019, India
     

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We construct some families of quadratic fields whose class numbers are divisible by 3. The main tools used are a trinomial introduced by Kishi and a parametrization of Kishi and Miyake of a family of quadratic fields whose class numbers are divisible by 3. At the end we compute class number of these fields for some small values and verify our results.
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  • Divisibility of Class Numbers of Certain Families of Quadratic Fields

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Authors

Azizul Hoque
Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211 019, India
Kalyan Chakraborty
Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211 019, India

Abstract


We construct some families of quadratic fields whose class numbers are divisible by 3. The main tools used are a trinomial introduced by Kishi and a parametrization of Kishi and Miyake of a family of quadratic fields whose class numbers are divisible by 3. At the end we compute class number of these fields for some small values and verify our results.

References