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Transactions of the American Mathematical Society

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Eigenfunctions of the Laplacian acting on degree zero bundles over special Riemann surfaces

Author: Marco Matone
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 2989-3004
MSC (2000): Primary 14H55; Secondary 11F72
Published electronically: March 23, 2004
MathSciNet review: 2052938
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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

Marco Matone
Affiliation: Department of Physics “G. Galilei” - Istituto Nazionale di Fisica Nucleare, University of Padova, Via Marzolo, 8 - 35131 Padova, Italy

Received by editor(s): February 1, 2002
Published electronically: March 23, 2004
Article copyright: © Copyright 2004 American Mathematical Society