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

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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.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.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…

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 M11​ and J1​ extensions

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

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