On the parity of the class number of the $7ⁿ$th cyclotomic field

Year, pages: 2009, 357 - 364

For an odd prime number $p$ and an integer $n ≥ 0$, let $h_n$ be the class number of the $pⁿ⁺¹$st cyclotomic field $\Q(ζ_pⁿ⁺¹)$. It is known that when $p=3$ or $5$, $h_n$ is odd for all $n ≥ 0$. We prove that the same holds also when $p=7$.

Ichimura, H. 2009. On the parity of the class number of the $7ⁿ$th cyclotomic field. In Mathematica Slovaca, vol. 59, no.3, pp. 357-364. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0132-5

Ichimura, H. (2009). On the parity of the class number of the $7ⁿ$th cyclotomic field. Mathematica Slovaca, 59(3), 357-364. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0132-5