arXiv subjects

Yoshichika Iizuka

Publications and source records attributed to Yoshichika Iizuka.

2 recordsLinked to original sources

arXiv2026

Infinite families of pairs of real quadratic fields whose class numbers are divisible by a given integer

For any integers \(N \ge 2\) and \(m \ge 1\), we prove that there exist infinitely many pairs of real quadratic fields \(\QQ(\sqrt{D}), \QQ(\sqrt{D + m})\), with \(D \in \ZZ\) and \(D > 0\), such that the class numbers of both fields are divisible by \(N\). Write \(N = 2^{e}n\) with \(n\) odd. If \(n > 1\), then the class groups of both fields in each such pair contain an element of order \(n\).

math.NT↗

arXiv2026

An infinite family of pairs of distinct quartic Galois CM-fields with the same discriminant and regulator

We construct an infinite family of pairs of distinct imaginary biquadratic fields and pairs of distinct imaginary cyclic quartic fields with the same discriminant and regulator. We also construct an infinite family of imaginary biquadratic fields and imaginary cyclic quartic fields with the same regulator. Moreover, we give examples of a pair of distinct imaginary biquadratic fields and a pair of distinct imaginary cyclic quartic fields with the same discriminant, regulator and class number.

math.NT↗