Miho Aoki

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math.NT2026

Chebyshev's Bias against Splitting and Principal Primes in Global Fields

Miho Aoki, Shin-ya Koyama

Reasons for the emergence of Chebyshev's bias were investigated. The Deep Riemann Hypothesis (DRH) enables us to reveal that the bias is a natural phenomenon for achieving a well-b…

math.NT2024

Galois module structure of algebraic integers of the simplest cubic field

Hajime Ogawa, Miho Aoki

Let $L_{n}$ be a simplest cubic field with Galois group $G = Gal (L_{n} / Q)$ . The associated order is denoted as ${\cal A}_{L_n/\mathbb Q}:= \{ x\in {\mathbb Q} [G] \, |\, x…

math.NT2024

Normal integral bases of Lehmer's cyclic quintic fields

Yu Hashimoto, Miho Aoki

Let $K_{n}$ be a tamely ramified cyclic quintic field generated by a root of Emma Lehmer's parametric polynomial. We give all normal integral bases for $K_{n}$ only by the roots of the…