T. Itoh

activity

20082026

most citedOn the Z_p-ranks of tamely ramified Iwasawa modules

12 citations · 13 across the 8 of their papers we have counts for

collaborators

8 papers

math.NT2026

Abelian $p$ -extensions with restricted $p$ -ramification and the cyclotomic $Z_{2}$ -extension of $Q (q)$

Tsuyoshi Itoh, Naoki Kumakawa

We develop Hachimori's study on the unramified Iwasawa modules using extensions with restricted $p$ -ramification. Let $K$ be an algebraic number field, and $p$ a prime number which…

math.NT2024

Class number behavior in a two-tiered tower of $Z_{p}$ -extensions

Tsuyoshi Itoh

Let $k_{\infty}$ be the cyclotomic $Z_{p}$ -extension field of an algebraic number field $k$ . Moreover, we take a $Z_{p}$ -extension $K_{\infty}$ over $k_{\infty}$ . In this p…

math.NT2022

A remark on Greenberg's generalized conjecture for imaginary $S_{3}$ -extensions of $Q$

Tsuyoshi Itoh

Let $K / Q$ be an imaginary $S_{3}$ -extension, and $p$ a prime number which splits into exactly three primes in $K$ . We give a sufficient condition for the validity of Greenb…

math.NT2020

On the unramified Iwasawa module of a $Z_{p}$ -extension generated by division points of a CM elliptic curve

Tsuyoshi Itoh

We consider the unramified Iwasawa module $X (F_{\infty})$ of a certain $Z_{p}$ -extension $F_{\infty} / F_{0}$ generated by division points of an elliptic curve with complex multipl…

math.NT2018

On the structure of the Galois group of the maximal pro- $p$ extension with restricted ramification over the cyclotomic $Z_{p}$ -extension

Tsuyoshi Itoh

Let $k_{\infty}$ be the cyclotomic $Z_{p}$ -extension of an algebraic number field $k$ . We denote by $S$ a finite set of prime numbers which does not contain $p$ , and $S(k_\inf…

math.NT2011★ 1 cited

On tamely ramified Iwasawa modules for the cyclotomic Z_p-extension of abelian fields

Tsuyoshi Itoh

Let p be an odd prime, and k_\infty the cyclotomic Z_p-extension of an abelian field k. For a finite set S of rational primes which does not include p, we will consider the maximal…

math.NT2011★ 12 cited

On the Z_p-ranks of tamely ramified Iwasawa modules

Tsuyoshi Itoh, Yasushi Mizusawa, Manabu Ozaki

For a prime number p, we denote by K the cyclotomic Z_p-extension of a number field k. For a finite set S of prime numbers, we consider the S-ramified Iwasawa module which is the G…

math.NT2008

Unramified extensions and geometric $Z_{p}$ -extensions of global function fields

Tsuyoshi Itoh

We study on finite unramified extensions of global function fields (function fields of one valuable over a finite field). We show two results. One is an extension of Perret's resul…

Abelian p-extensions with restricted p-ramification and the cyclotomic Z2​-extension of Q(q​)

Class number behavior in a two-tiered tower of Zp​-extensions

A remark on Greenberg's generalized conjecture for imaginary S3​-extensions of Q

On the unramified Iwasawa module of a Zp​-extension generated by division points of a CM elliptic curve

On the structure of the Galois group of the maximal pro-p extension with restricted ramification over the cyclotomic Zp​-extension

On tamely ramified Iwasawa modules for the cyclotomic Z_p-extension of abelian fields

On the Z_p-ranks of tamely ramified Iwasawa modules

Unramified extensions and geometric Zp​-extensions of global function fields

Abelian $p$ -extensions with restricted $p$ -ramification and the cyclotomic $Z_{2}$ -extension of $Q (q)$

Class number behavior in a two-tiered tower of $Z_{p}$ -extensions

A remark on Greenberg's generalized conjecture for imaginary $S_{3}$ -extensions of $Q$

On the unramified Iwasawa module of a $Z_{p}$ -extension generated by division points of a CM elliptic curve

On the structure of the Galois group of the maximal pro- $p$ extension with restricted ramification over the cyclotomic $Z_{p}$ -extension

Unramified extensions and geometric $Z_{p}$ -extensions of global function fields