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Pratik Rao

Publications and source records attributed to Pratik Rao.

2 recordsLinked to original sources
arXiv2026

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

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.

math.NT↗
arXiv2026

On the class number of certain cyclotomic fields

We construct four infinite families of cyclotomic fields and show that each member of these families has class number a multiple of 3. In fact, we show that the class number of the corresponding maximal real subfields has class number divisible by 3. A construction by Kishi and Miyake [11] and a result of Yamaguchi [13] help us achieve this target. Finally, we produce computational evidence corroborating our results.

math.NT↗