Hold Date

2010-11-18 16:00～2010-11-18 17:00

Place

Lecture Room S-2, Faculty of Mathematics building, Ito Campus

Object person

　

Speaker

Takashi ONO (Johns Hopkins University)

summary:
The talk belongs to a relatively new scenario in number theory.
Let K/k be a Galois extension of number fields. The main idea is to borrow
a method of Poincare on automorphic functions to do  number theory by
replacing the ring R of holomorphic functions on the upper half plane by the
ring of algebraic integers of K and the modular group G acting on R by the
Galois group of K/k.
It turns out that the  index of space of Poincare series in the  space of
modular forms ( for a given weight) corresponds to a kind of "index"
involving invariants in ramification theory of Galois extensions.