Student Number Theory seminar

Speaker

Shuntaro Yamagishi, Department of Pure Mathematics, University of Waterloo

A Fundamental Region for Hecke's Modular Group: Abstract

Hecke proved analytically that when \lambda\geq 2 or when \lambda=2 cos(\pi=q), q\in\mathbb{Z}, q \geq 3, then B(\lambda) = {\tau\in\mathbb{H} : |Re \tau| < \lambda/2, |\tau| > 1} is a fundamental region for the group G(\lambda) =< S_\lambda; T >, where S_\lambda : \lambda \rightarrow \tau + \lambda and T : \tau \rightarrow -1/\tau. He also showed that B(\lambda) fails to be a fundamental region for all other \lambda > 0 by proving that G(\lambda) is not discontinuous. In his paper "A Fundamental Region for Hecke's Modular Group", Ronald Evans gave an elementary proof of these facts. In this talk I will give an introduction to this paper.