2017arXiv (Cornell University)Open access

Divisibility of class numbers of certain families of quadratic fields

Azizul Hoque, Kalyan Sekhar Chakraborty

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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.

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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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Available 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.

Key concepts: Divisibility rule, Trinomial, Mathematics, Class (philosophy), Quadratic equation, Parametrization (atmospheric modeling), Infinite divisibility, Construct (python library)

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