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arXiv · 2609.16678

An infinite family of imaginary biquadratic fields with a large class number

Kalyan Chakraborty·Pratik Rao·Aishwarya Dabhole
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Abstract

We construct an infinite family of imaginary biquadratic fields with large class numbers. The construction of this family is done by composing two distinct families of imaginary quadratic fields: the first one is the family Q(sqrt(k^2-p^l)) introduced by Banerjee and Hoque [1], subject to specific constraints on the integer parameters, l, k and p, and the second one is the parametrized family of the form Q(sqrt(-F_(50s+25))) based on Fibonacci numbers, introduced by Kishi [2]. One of the main tools that is used is Kuroda's class number formula of imaginary biquadratic fields. We choose these two families with the sole aim to get high order elements in the class group of the resultant biquadratic fields.

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Kalyan Chakraborty, Pratik Rao, Aishwarya Dabhole. 2026-09-15. An infinite family of imaginary biquadratic fields with a large class number. https://arxiv.org/abs/2609.16678

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