1 citations · 1 across the 5 of their papers we have counts for
5 papers
On the triviality of the unramified Iwasawa modules of the maximal multiple -extensions
Keiji Okano
For a number field and an odd prime number , we consider the maximal multiple -extension of and the unramified Iwasawa module , w…
On the Cyclicity of the Unramified Iwasawa Modules of the Maximal Multiple -Extensions Over Imaginary Quadratic Fields
Takashi Miura, Kazuaki Murakami, Keiji Okano +1
For an odd prime number , we study the number of generators of the unramified Iwasawa modules of the maximal multiple -extensions over Iwasawa algebra. In a previo…
Galois coinvariants of the unramified Iwasawa modules of multiple -extensions
Takashi Miura, Kazuaki Murakami, Rei Otsuki +1
For a CM-field and an odd prime number , let be a certain multiple -extension of . In this paper, we study several basic properties of the u…
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 conditions for ρ-value is 1 or not of complete family of pairing-friendly elliptic curves
Keiji Okano
We study whether a complete family of pairing friendly elliptic curves has a ρ-value 1 or not. We show that, in some cases, ρ-values are not to be 1.