Yutaka Konomi | Searcharxiv

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↗

arXiv2025

On group rings of the simple group of order 168, 504 or 360 and their modules

Let $p$ be a prime and $\mathbb{Z}_p$ the ring of $p$-adic integers. Let $G$ denote the simple group of order 168, 504 or 360. In this paper, we study the structure of the $χ$-part of a $\mathbb{Z}_p[\mathrm{Im}(χ)][G]$-module come from ideal class groups, Artin $L$-functions and Iwasawa theory.

math.NT↗