A. Yamasaki

activity

20092026

most citedRationality problem for algebraic tori

19 citations · 30 across the 22 of their papers we have counts for

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7 papers · 1 filter

math.NT2025

Hasse norm principle for Heisenberg extensions of degree $p^{3}$

Akinari Hoshi, Aiichi Yamasaki

Let $k$ be a global field and $p$ be an odd prime number. We give a necessary and sufficient condition for the Hasse norm principle for separable field extensions $K / k$ , i.e. the d…

math.NT2025

Hasse norm principle for metacyclic extensions with trivial Schur multiplier

Akinari Hoshi, Aiichi Yamasaki

Let $k$ be a global field, $K / k$ be a finite separable field extension and $L / k$ be the Galois closure of $K / k$ with Galois groups $G = Gal (L / k)$ and $H = Gal (L / K) ⪇ G$ .…

math.NT2024

Norm one tori and Hasse norm principle, III: Degree $16$ case

Akinari Hoshi, Kazuki Kanai, Aiichi Yamasaki

Let $k$ be a field, $T$ be an algebraic $k$ -torus, $X$ be a smooth $k$ -compactification of $T$ and $Pic X$ be the Picard group of $\overline{X}=X\times_k\overline…

math.NT2022

Hasse norm principle for $M_{11}$ and $J_{1}$ extensions

Akinari Hoshi, Kazuki Kanai, Aiichi Yamasaki

We give a necessary and sufficient condition for the Hasse norm principle for field extensions $K / k$ when the Galois groups $Gal (L / k)$ of the Galois closure $L / k$ of $K / k$ ar…

math.NT2015★ 1 cited

Rationality problems for relation modules of dihedral groups

Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

Let D_n be the dihedral group of order 2n where n \ge 2, 1 \to R \to F \to D_n \to 1 be a free presentation of D_n. R^{ab}:=R/[R,R] becomes a \bm{Z}[D_n]-lattice. We will study the…

math.NT2014

Class Numbers and Algebraic Tori

Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

Let $p$ be an odd prime number, $D_{p}$ be the dihedral group of order $2 p$ , $h_{p}$ and $h_{p}^{+}$ be the class numbers of $Q (ζ_{p})$ and $Q (ζ_{p} + ζ_{p}^{- 1})$ respectively. Theorem…

math.NT2009

Negative solutions to three-dimensional monomial Noether problem

Aiichi Yamasaki

Three-dimensional monomial Noether problem can have negative solutions for 8 groups by the suitable choice of the coefficients. We find the necessary and sufficient condition for t…

Hasse norm principle for Heisenberg extensions of degree p3