Let p be a prime number. It is an interesting problem to consider whether a prime number ℓ divides the class numbers of the intermediate fields of the cyclotomic Zp‐extension of Q. In the case p = 2, R. Okazaki developed a theory for this problem by using Mahler measure. In this paper, we focus on the case p = 3 and show that a prime number ℓ does not divide the class numbers of the intermediate fields of the cyclotomic Z33‐extension of Q if ℓ satisfies ℓ≢±1 mod 27.

This content is only available via PDF.
You do not currently have access to this content.