Postcards from the Edge, or Snapshots of the Theory of Generalised Moonshine
Printed: Dec 2002
We begin by reviewing Monstrous Moonshine. The impact of Moonshine on
algebra has been profound, but so far it has had little to teach
number theory. We introduce (using `postcards') a much larger context
in which Monstrous Moonshine naturally sits. This context suggests
Moonshine should indeed have consequences for number theory. We
provide some humble examples of this: new generalisations of Gauss
sums and quadratic reciprocity.
11F22 - Relationship to Lie algebras and finite simple groups
17B67 - Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
81T40 - Two-dimensional field theories, conformal field theories, etc.