Akinari Hoshi

activity

20242026

collaborators

8 papers

math.AG2026

Rationality problem for norm one tori of tensor products of Ã©tale 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 Ã©tale $k$ -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 $L_{m} = Q (I^\pm)$ be the simplest cubic field with class number $h_{m}$ and conductor $f_{m}$ where $I^\pm$ is a root of $f_m(X)=X^3-m…

math.AG2025

Birational classification for algebraic tori

Akinari Hoshi, Aiichi Yamasaki

We give a stably birational classification for algebraic tori of dimensions $3$ and $4$ over a field $k$ . First, we define the weak stably equivalence of algebraic tori and show th…

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.AG2025

Rationality problem for norm one tori for $A_{5}$ and $PSL_{2} (F_{8})$ extensions

Akinari Hoshi, Aiichi Yamasaki

We give a complete answer to the rationality problem (up to stable $k$ -equivalence) for norm one tori $T = R_{K / k}^{(1)} (G_{m})$ of $K / k$ whose Galois closures $L / k$ are $A_5\…

Rationality problem for norm one tori of tensor products of Ã©tale algebras and Hasse norm principle

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

Simplest cubic fields with small class number

Birational classification for algebraic tori

Hasse norm principle for metacyclic extensions with trivial Schur multiplier

Rationality problem for norm one tori for A5​ and PSL2​(F8​) extensions

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

Rationality problem for norm one tori for $A_{5}$ and $PSL_{2} (F_{8})$ extensions