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In this paper, we revisit the connection between the Riemann-Roch theorem andthe zero energy solutions of the two-dimensional Dirac equation in the presenceof a delta-function like magnetic field. Our main result is the resolution of aparadox - the fact that the Riemann-Roch theorem correctly predicts the numberof zero energy solutions of the Dirac equation despite counting what seems tobe the wrong type of functions.

The Riemann-Roch Theorem and Zero Energy Solutions of the Dirac Equation on the Riemann Sphere