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Postcards from the Edge, or Snapshots of the Theory of Generalised Moonshine

Published online by Cambridge University Press:  20 November 2018

Terry Gannon
Terry Gannon*
Affiliation:
Department of Mathematical Sciences University of Alberta Edmonton, Alberta T6G 2G1, email: [email protected]
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Abstract

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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.

Keywords

11F2217B6781T40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 4 , 01 December 2002 , pp. 606 - 622
Copyright
Copyright © Canadian Mathematical Society 2002

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