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)....

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...

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...

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 ...