Kodai Mathematical Journal
Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991
On class numbers inside the real pth cyclotomic field
Humio Ichimura
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2024 Volume 47 Issue 1 Pages 11-33

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Abstract

We fix an integer n ≥ 1, a prime number with 2n and an integer s ≥ 0. We deal with a prime number p of the form p = 2nℓf + 1. For 0 ≤ tf, let Kt be the real cyclic field of degree t contained in the pth cyclotomic field, and let ht be the class number of Kt. We show that when p (or f) is large enough with respect to n, and s, a prime number r does not divide the ratio hf/hf - (s + 1) whenever r is a primitive root modulo 2.

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© 2024 Department of Mathematics, Tokyo Institute of Technology
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