Eigenfunctions of the Laplacian Acting on Degree Zero Bundles over Special Riemann Surfaces
Algebraic Geometry
2018-05-29 v3 High Energy Physics - Theory
Mathematical Physics
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.
Keywords
Cite
@article{arxiv.math/0105051,
title = {Eigenfunctions of the Laplacian Acting on Degree Zero Bundles over Special Riemann Surfaces},
author = {Marco Matone},
journal= {arXiv preprint arXiv:math/0105051},
year = {2018}
}
Comments
20 pages, LaTeX. Subsection added on the relation between special Riemann surfaces and Jacobians with complex multiplication, typos corrected, one reference added. v3. Final version to appear in Trans.Am.Math.Soc