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Generalized Kac-Moody algebras, automorphic forms and Conway's group II
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Nils R. Scheithauer
Published/Copyright:
November 18, 2008
Let Γ be a genus 0 group between Γ0(N) and its normalizer in SL2(ℝ) where N is squarefree. We construct an automorphic product on Γ × Γ and determine its sum expansions at the different cusps. We obtain many new product identities generalizing the classical product formula of the elliptic j-function due to Zagier, Borcherds and others. These results imply that the moonshine conjecture for Conway's group Co0 is true for elements of squarefree level.
Received: 2006-03-24
Revised: 2007-08-13
Published Online: 2008-11-18
Published in Print: 2008-December
© Walter de Gruyter Berlin · New York 2008
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Articles in the same Issue
- On mixing and ergodicity in locally compact motion groups
- Path integrals on manifolds by finite dimensional approximation
- The Schwartz algebra of an affine Hecke algebra
- Adelic amoebas disjoint from open halfspaces
- Generalized Kac-Moody algebras, automorphic forms and Conway's group II
- A Siegel-Weil formula for automorphic characters: Cubic variation of a theme of Snitz
- Calibrated manifolds and Gauge theory
- On the gradient set of Lipschitz maps
