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arXiv · 2408.05157

Bi-quadratic Pólya fields with five distinct ramified primes

Md. Imdadul Islam·Jaitra Chattopadhyay·Debopam Chakraborty
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Abstract

For an algebraic number field $K$, the Pólya group of $K$, denoted by $Po(K),$ is the subgroup of the ideal class group $Cl_{K}$ generated by the ideal classes of the products of prime ideals of same norm. The number field $K$ is said to be Pólya if $Po(K)$ is trivial. Motivated by several recent studies on the group $Po(K)$ when $K$ is a totally real bi-quadratic field, we investigate the same with five distinct odd primes ramifying in $K/\mathbb{Q}$. This extends the previous results on this problem, where the number of distinct ramified primes was at most four.

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Md. Imdadul Islam, Jaitra Chattopadhyay, Debopam Chakraborty. 2024-08-09. Bi-quadratic Pólya fields with five distinct ramified primes. https://arxiv.org/abs/2408.05157

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