Transactions of the American Mathematical Society

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

Author(s): Marco Matone
Journal: Trans. Amer. Math. Soc. 356 (2004), 2989-3004.
MSC (2000): Primary 14H55; Secondary 11F72
Posted: March 23, 2004
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14H55, 11F72

Marco Matone
Affiliation: Department of Physics ``G. Galilei'' - Istituto Nazionale di Fisica Nucleare, University of Padova, Via Marzolo, 8 - 35131 Padova, Italy
Email: matone@pd.infn.it

DOI: 10.1090/S0002-9947-04-03587-1
PII: S 0002-9947(04)03587-1
Received by editor(s): February 1, 2002
Posted: March 23, 2004
Copyright of article: Copyright 2004, American Mathematical Society

Marco Matone, The affine connection of supersymmetric SO(N)/Sp(N) theories, JHEP 0310 (2003), 068.

Gaetano Bertoldi, Stefano Bolognesi, Marco Matone, Luca Mazzucato, Yu Nakayama, THE LIOUVILLE GEOMETRY OF N = 2 INSTANTONS AND THE MODULI OF PUNCTURED SPHERES, JHEP 0405 (2004), 075. (English)

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