## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Tuesday, May 15, 2012 — 10:00 AM EDT

Shuntaro Yamagishi, Department of Pure Mathematics, University of Waterloo

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.

Location

MC - Mathematics & Computer Building

5046

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.