A fundamental region for Hecke's modular group

A Fundamental Region for Hecke’s Modular Group

Hecke proved analytically that when h > 2 or when h = 2 CDS (m/q), q E Z, q > 3, then B(h) = (7: Im I > 0, / Re 7 1 < h/2, [ 7 j > 1) is a fundamental region for the group G(h) = (SA , T), where S,+ : 7 --f 7 + X and T: 7 ---t -l/~. He also showed that B(A) fails to be a fundamental region for all other A > 0 by proving that G(X) is not discontinuous. We give an elementary proof of these facts ...

A Proposed Model for Evaluating Modular Education

Introduction: Educational evaluation is one of the main elements of educational systems. It also has a particular role in different educational standards such as ISO 10015. It seems that oral and written examinations are not enough for an effective evaluation of instructions. In order to accomplish an efficient educational evaluation, an evaluation model was designed for educational assessment ...

Equation of state of gluon plasma from a fundamental modular region.

Despite considerable practical success in dealing with the gluon plasma, finite-temperature perturbation theory suffers at the fundamental level from infrared divergences discovered by Linde. However, if gauge or Gribov copies are properly eliminated from the physical state space, infrared modes are strongly suppressed. We describe the gluon plasma in zeroth order as a gas of free quasiparticle...

The Fundamental Region for a Fuchsian Group* by L. R. Ford

An Explicit Fundamental Domain for the Picard Modular Group in Two Complex Dimensions

Our main goal in this paper is to construct the first explicit fundamental domain of the Picard modular group acting on the complex hyperbolic space CH . The complex hyperbolic space is a Hermitian symmetric space, its bounded realization is the unit ball in C equipped with the Bergman metric. The Picard modular group is a discontinuous holomorphic automorphism subgroup of SU(2, 1) with Gaussia...