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Eigenfunctions of the Laplacian Acting on Degree Zero Bundles over Special Riemann Surfaces | | Marco Matone
; | | Date: |
7 May 2001 | | Journal: | Trans.Am.Math.Soc. 356 (2004) 2989-3004 | | Subject: | Algebraic Geometry; Mathematical Physics MSC-class: 14H99 (Primary), 11F99 (Secondary) | math.AG hep-th math-ph math.MP | | Abstract: | We find an infinite set of eigenfunctions for the Laplacian with respect to a flat metric with conical singularities and acting on degree zero bundles over special Riemann surfaces of genus greater than one. These special surfaces correspond to Riemann period matrices satisfying a set of equations which lead to a number theoretical problem. It turns out that these surfaces precisely correspond to branched covering of the torus. This reflects in a Jacobian with a particular kind of complex multiplication. | | Source: | arXiv, math.AG/0105051 | | Services: | Forum | Review | PDF | Favorites | |
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