n Conway and Norton's "Monstrous Moonshine" paper, it was proposed that each conjugacy class of elements m of the Monster group M could be associated with a modular function ;It was also observed that certain replication formulae seemed to hold between the functions ;This thesis is concerned with three main results. First, Conway and Norton observed that the general modular groups involved in the monstrous functions were certain normal subgroups of index h in ;Second, we observe that certain special cases of the replication formulae can be expressed using the well-known Hecke operator ;Finally we show, as a consequence of the replication formulae, an easy proof that the coefficients ;It should be remarked that most of the connections between the Monster and modular functions observed in "Monstrous Moonshine" have remained conjectural until now. In particular, this thesis contains the first proof of the replication formulae for the Monstrous functions, and the first computer-free proof that the
展开▼
