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Discrete Riemann surfaces: linear discretization and its convergence

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 Added by Mikhail Skopenkov
 Publication date 2012
  fields
and research's language is English




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We develop linear discretization of complex analysis, originally introduced by R. Isaacs, J. Ferrand, R. Duffin, and C. Mercat. We prove convergence of discrete period matrices and discrete Abelian integrals to their continuous counterparts. We also prove a discrete counterpart of the Riemann--Roch theorem. The proofs use energy estimates inspired by electrical networks.



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156 - Feng Luo , Jian Sun , Tianqi Wu 2020
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