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

Yoshichika Iizuka; Yutaka Konomi

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arXiv · 2506.23541

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

Yoshichika Iizuka·Yutaka Konomi

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Abstract

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.

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Yoshichika Iizuka, Yutaka Konomi. 2025-06-30. An infinite family of pairs of distinct quartic Galois CM-fields with the same discriminant and regulator. https://arxiv.org/abs/2506.23541

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