Naoto Dainobu

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20222025

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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…

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

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