Akinari Hoshi

activity

20072026

most citedRationality problem for algebraic tori

19 citations · 81 across the 44 of their papers we have counts for

collaborators

45 papers

math.AG2026

Rationality problem for norm one tori of tensor products of étale algebras and Hasse norm principle

Mathieu Florence, Akinari Hoshi, Aiichi Yamasaki

Let $k$ be a field. Let $A = \prod_{i = 1}^{r} K_{i}$ and $B = \prod_{j = 1}^{s} E_{j}$ be étale $k$ -algebras where $K_{i}$ and $E_{j}$ are finite separable field extensions of $k$ with $[K_{i} : k] = m_{i}$ …

math.NT2026

Multiplicative $f$ -ic forms on algebraic varieties arising from Thaine's generalized Jacobi sums

Akinari Hoshi, Kazuki Kanai

We study generalized Jacobi sums, cyclotomic numbers, and $d$ -compositions in Thaine's framework, and prove new multiplicative identities extending Davenport and Hasse's lifting th…

math.NT2026

Simplest cubic fields with small class number

Akinari Hoshi, Hiroaki Iida

Let $m \in Z$ be an integer and $L_{m} = Q (α)$ be the simplest cubic field with class number $h_{m}$ and conductor $f_{m}$ where $α$ is a root of $f_m(X)=X^3-mX^…

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…