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Discrete Riemann surfaces: linear discretization and its convergence. (English) Zbl 1358.30020

The authors develop a linear discretization in complex analysis. In particular they show the convergence of discrete period matrices and discrete abelian integrals to their continuous counterparts. Further they formulate and prove the discrete counterpart of the Riemann-Roch theorem. The proofs use energy estimates inspired by electrical networks.

MSC:

30G25 Discrete analytic functions
39A12 Discrete version of topics in analysis
31C20 Discrete potential theory

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References:

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