Kazuki Kanai

activity

20192026

most citedNorm one tori and Hasse norm principle

3 citations · 4 across the 9 of their papers we have counts for

collaborators

9 papers

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.AG2026

The rationality problem for multinorm one tori, II

Sumito Hasegawa, Kazuki Kanai, Yasuhiro Oki

We investigate the stable and retract rationality of multinorm one tori associated to finite {é}tale algebras. Our results are organized according to the greatest common divisor $d…

math.AG2025

The rationality problem for multinorm one tori

Sumito Hasegawa, Kazuki Kanai, Yasuhiro Oki

In this paper, we study the rationality problem for multinorm one tori, a natural generalization of norm one tori. For multinorm one tori that split over finite Galois extensions w…

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.GR2023

Uniform Cyclic Group Factorizations of Finite Groups

Kazuki Kanai, Kengo Miyamoto, Koji Nuida +1

In this paper, we introduce a kind of decomposition of a finite group called a uniform group factorization, as a generalization of exact factorizations of a finite group. A group $…

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.NT2021

Davenport and Hasse's theorems and lifts of multiplication matrices of Gaussian periods

Akinari Hoshi, Kazuki Kanai

Let $e \geq 2$ be an integer, $p^{r}$ be a prime power with $p^{r} \equiv 1 (mod e)$ and $η_{r} (i)$ be Gaussian periods of degree $e$ for $F_{p^{r}}$ . By the dual form of…

math.AG2020★ 1 cited

Norm one tori and Hasse norm principle, II: Degree $12$ 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.AG2019★ 3 cited

Norm one tori and Hasse norm principle

Akinari Hoshi, Kazuki Kanai, Aiichi Yamasaki

Let $k$ be a field and $T$ be an algebraic $k$ -torus. In 1969, over a global field $k$ , Voskresenskii proved that there exists an exact sequence $0\to A(T)\to H^1(k,{\rm Pic}\,\ove…

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

The rationality problem for multinorm one tori, II

The rationality problem for multinorm one tori

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

Uniform Cyclic Group Factorizations of Finite Groups

Hasse norm principle for M11​ and J1​ extensions

Davenport and Hasse's theorems and lifts of multiplication matrices of Gaussian periods

Norm one tori and Hasse norm principle, II: Degree 12 case

Norm one tori and Hasse norm principle

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

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

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

Norm one tori and Hasse norm principle, II: Degree $12$ case