We consider the matrix regularization of scalar fields on a Riemann surface with general gauge-field background. propose construction fuzzy version Laplacian.Received 23 March 2021Accepted 30 April 2021DOI:https://doi.org/10.1103/PhysRevD.103.126003Published by American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution this work must maint...

We find an infinite set of eigenfunctions for the Laplacian 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 leads to a number theoretical problem.