OZAKI, Manabu

J-GLOBAL         Last updated: Oct 10, 2019 at 02:49
OZAKI, Manabu
Waseda University
Faculty of Science and Engineering School of Fundamental Science and Engineering
Job title
Research funding number

Research Areas


Published Papers

Non-abelian Iwasawa theory of Z_p-extensions--Overview and outlook
RIMS Kokyuroku Bessatsu   B64 313-330   Mar 2017   [Refereed]
Anderson, Daniel D.; Aoki, Takashi; Izumi, Shuzo; Ohno, Yasuo; Ozaki, Manabu
Tamkang Journal of Mathematics   47(3) 261-270   Sep 2016
Let A1, . . . , An (n ≥ 2) be elements of an commutative multiplicative lattice. Let G(k) (resp., L(k)) denote the product of all the joins (resp., meets) of k of the elements. Then we show that L(n)G(2)G(4) ···G(2[n/2]) ≤ G(1)G(3) ···G(2[n/2]-1)....
Fukuda, Takashi; Komatsu, Keiichi; Ozaki, Manabu; Tsuji, Takae
Functiones et Approximatio, Commentarii Mathematici   54(1) 7-17   Jan 2016   [Refereed]
In the preceding papers, two of authors developed criteria for Greenberg conjecture of the cyclotomic Z2-extension of k = Q(√p ) with prime number p. Criteria and numerical algorithm in [5], [3] and [6] enable us to show λ2(k) = 0 for all p less t...
Anderson, D. D.;Izumi, Shuzo;Ohno, Yasuo;Ozaki, Manabu
Mizusawa, Yasushi;Ozaki, Manabu
MATHEMATISCHE ZEITSCHRIFT   273(3-4) 1161-1173   2013

Research Grants & Projects

Non-abelian extensions of number fields with restricted ramification
Project Year: Apr 2013 - Mar 2016
In this research project, we obtain the followoing results: 1.A generalization of the Neukirch-Uchida Theorem to number fields of infinite degree, 2.Criterion of arithmetically equivalence in terms of Iwasawa modules with restricted ramification, ...
Study of non-abelian number theory based on Iwasawa theory
Project Year: Apr 2009 - Mar 2013
In this research project, I have obtained results on (1) a formula describing Z_p-rank of tamely ramified Iwasawa modules of the basic Z_p-extension, (2) an analogy of Weil paring for ideal class groups of number fields, (3) the isomorphism classe...
Project Year: 1997 - 1999
In 1994 Wiles and Taylor have settled the proof of Taniyama-Shimura conjecture for (semistable) elliptic curves over Q. This, with its application to the proof of Fermat's Last Theorem, was one of the greatest achievment in this century. In our pr...
Development of non-abelian Iwasawa theory
Combinatorial semigroup theory and its applications
(1)Amalgamation problems for groups are strongly connected with word problems for groups, Especially, through amalgamation products of groups。 Consequently, many word problems for groups have been solved and many nice results have been brought by ...