【My research seeds】
○The study on the relation of between the Fitting ideals of the minus part of the ideal class groups of CM-fields which is abelian over totally real number fields and the Stickelberger elements defined by the special values of partial zeta functions.
○The study on the T-modified ideal class groups and its application to Brumer-Stark conjecture.
○Mazur-Tate conjecture.
Galois action on the ideal class groups of CM fields
Massage:
In number theory, it is very important to study the ideal class group, which measures how far the ring of integers of a number field from the principal ideal domain.
I’m interested in the action of the Galois group on the ideal class group, and study a refinement of Iwasawa theory and Brumer-Stark conjecture.
e-mail： [email protected]
Examples of mysterious relations between ideal class groups and values of zeta functions Class Number Formula
Stickelberger’s Theorem
Iwasawa Main Conjecture Specialized field: Mathematics
Keyword: Algebraic number theory, Iwasawa theory, Ideal class group, p-adic L-function
Takashi MIURA
Dept. of General Science Doctor of Science
