K. Okano

activity

20162021

collaborators

3 papers

math.NT2021

On the Cyclicity of the Unramified Iwasawa Modules of the Maximal Multiple $Z_{p}$ -Extensions Over Imaginary Quadratic Fields

Takashi Miura, Kazuaki Murakami, Keiji Okano +1

For an odd prime number $p$ , we study the number of generators of the unramified Iwasawa modules of the maximal multiple $Z_{p}$ -extensions over Iwasawa algebra. In a previo…

math.NT2019

Galois coinvariants of the unramified Iwasawa modules of multiple $Z_{p}$ -extensions

Takashi Miura, Kazuaki Murakami, Rei Otsuki +1

For a CM-field $K$ and an odd prime number $p$ , let $K^{'}$ be a certain multiple $Z_{p}$ -extension of $K$ . In this paper, we study several basic properties of the u…

cs.CR2016

Note on families of pairing-friendly elliptic curves with small embedding degree

Keiji Okano

Pairing-based cryptographic schemes require so-called pairing-friendly elliptic curves, which have special properties. The set of pairing-friendly elliptic curves that are generate…

On the Cyclicity of the Unramified Iwasawa Modules of the Maximal Multiple Zp​-Extensions Over Imaginary Quadratic Fields

Galois coinvariants of the unramified Iwasawa modules of multiple Zp​-extensions

Note on families of pairing-friendly elliptic curves with small embedding degree

On the Cyclicity of the Unramified Iwasawa Modules of the Maximal Multiple $Z_{p}$ -Extensions Over Imaginary Quadratic Fields

Galois coinvariants of the unramified Iwasawa modules of multiple $Z_{p}$ -extensions