Bi-quadratic Pólya fields with five distinct ramified primes

2024/08/09 by Islam, Md. Imdadul, Chattopadhyay, Jaitra, Chakraborty, Debopam · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2408.05157

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/ℚ. This extends the previous results on this problem, where the number of distinct ramified primes was at most four.

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