Naoto Dainobu

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20222025

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math.NT2025

On the local equivariant Tamagawa number conjecture for Tate motives

Mahiro Atsuta, Naoto Dainobu, Takenori Kataoka

The local equivariant Tamagawa number conjecture (local ETNC) for a motive predicts a precise relationship between the local arithmetic complex and the root numbers which appear in…

math.NT2024

On $p$ -adic $L$ -functions of elliptic curves and the ideal class groups of the division fields

Naoto Dainobu

Let $E$ be an elliptic curve defined over $Q$ and $F$ be $Q$ or an imaginary quadratic field with certain conditions. In this article, we study the ideal class gr…

math.NT2023

Ideal class groups of division fields of elliptic curves and everywhere unramified rational points

Naoto Dainobu

Let $E$ be an elliptic curve over $Q$ , $p$ an odd prime number and $n$ a positive integer. In this article, we investigate the ideal class group $\mathrm{Cl}(\mathbb{Q}(E[…

math.NT2022

Elliptic analogue of irregular prime numbers for the $p^{n}$ -division fields of the curves $y^{2} = x^{3} - (s^{4} + t^{2}) x$

Naoto Dainobu, Yoshinosuke Hirakawa, Hideki Matsumura

A prime number $p$ is said to be irregular if it divides the class number of the $p$ -th cyclotomic field $Q (ζ_{p}) = Q (G_{m} [p])$ . In this paper, we study…

math.NT2022

On an explicit reciprocity law in local class field theory via $(φ, Γ)$ -modules

Naoto Dainobu

Let $K$ be an unramified extension of $Q_{2}$ and $μ_{2^{n}}$ the group of $2^{n}$ -th root of unity for a fixed integer $n ⩾ 2$ . In this paper, we give an explicit formul…

math.NT2022

Ideal class groups of number fields associated to modular Galois representations

Naoto Dainobu

Let $p$ be an odd prime number and $f$ a modular form. We consider the $F_{p}$ -valued Galois representation $ρ ˉ_{f}$ attached to $f$ and its twist $ρ ˉ_{f, D}$ by the qua…

math.NT2022

Ideal class groups of number fields and Bloch-Kato's Tate-Shafarevich groups for symmetric powers of elliptic curves

Naoto Dainobu

For an elliptic curve $E$ over $Q$ , putting $K = Q (E [p])$ which is the $p$ -th division field of $E$ for an odd prime $p$ , we study the ideal class group $\mathrm{Cl…

On the local equivariant Tamagawa number conjecture for Tate motives

On p-adic L-functions of elliptic curves and the ideal class groups of the division fields

Ideal class groups of division fields of elliptic curves and everywhere unramified rational points

Elliptic analogue of irregular prime numbers for the pn-division fields of the curves y2=x3−(s4+t2)x

On an explicit reciprocity law in local class field theory via (φ,Γ)-modules

Ideal class groups of number fields associated to modular Galois representations

Ideal class groups of number fields and Bloch-Kato's Tate-Shafarevich groups for symmetric powers of elliptic curves

On $p$ -adic $L$ -functions of elliptic curves and the ideal class groups of the division fields

Elliptic analogue of irregular prime numbers for the $p^{n}$ -division fields of the curves $y^{2} = x^{3} - (s^{4} + t^{2}) x$

On an explicit reciprocity law in local class field theory via $(φ, Γ)$ -modules