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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Eigenfunctions of the Laplacian acting on degree zero bundles over special Riemann surfaces
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by Marco Matone PDF
Trans. Amer. Math. Soc. 356 (2004), 2989-3004 Request permission

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
  • Email: matone@pd.infn.it
  • Received by editor(s): February 1, 2002
  • Published electronically: March 23, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 2989-3004
  • MSC (2000): Primary 14H55; Secondary 11F72
  • DOI: https://doi.org/10.1090/S0002-9947-04-03587-1
  • MathSciNet review: 2052938