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

@misc{chakraborty2026infinite,
  title = {{An infinite family of imaginary biquadratic fields with a large class number}},
  author = {Kalyan Chakraborty and Pratik Rao and Aishwarya Dabhole},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16678},
  eprint = {2609.16678},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16678},
}

TY  - UNPB
TI  - An infinite family of imaginary biquadratic fields with a large class number
AU  - Kalyan Chakraborty
AU  - Pratik Rao
AU  - Aishwarya Dabhole
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.16678
UR  - https://arxiv.org/abs/2609.16678
AB  - 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.
ER  -