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

2025/06/30 by Yoshichika Iizuka, Iizuka, Yoshichika, Yutaka Konomi +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Mathematical Dynamics and Fractals #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.2506.23541

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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