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2023•arXiv (Cornell University)Open access

On the plus parts of the class numbers of cyclotomic fields

Kalyan Chakraborty, Azizul Hoque

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Abstract

We exhibit some new families of cyclotomic fields which have non-trivial plus parts of their class numbers. We also prove the $3$ - divisibility of the plus part of the class number of another family consisting of infinitely many cyclotomic fields. At the end, we provide some numerical examples supporting our results.

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We exhibit some new families of cyclotomic fields which have non-trivial plus parts of their class numbers. We also prove the $3$ - divisibility of the plus part of the class number of another family consisting of infinitely many cyclotomic fields. At the end, we provide some numerical examples supporting our results.

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Available abstract

We exhibit some new families of cyclotomic fields which have non-trivial plus parts of their class numbers. We also prove the $3$ - divisibility of the plus part of the class number of another family consisting of infinitely many cyclotomic fields. At the end, we provide some numerical examples supporting our results.

Key concepts: Divisibility rule, Cyclotomic field, Class (philosophy), Mathematics, Class number, Field (mathematics), Pure mathematics, Arithmetic

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