@inbook{2b41f076407043ceb5529adde2288e39,

title = "A Riemann-Roch Theorem on Infinite Graphs",

abstract = "A Riemann-Roch theorem on graph was initiated by M.Baker and S.Norine. In their article, a Riemann-Roch theorem on a finite graph with uniform unit vertex-weight and uniform unit edge-weight was established and a feasibility of Riemann-Roch theorem on infinite graph was suggested. In this article, we take an edge-weighted infinite graph and focus on the importance of the spectral gaps of the Laplace operators defined on its finite subgraphs naturally given by ℚ -valued positive weights on the edges. We build a potential theoretic scheme for a proof of a Riemann-Roch theorem on the edge-weighted infinite graphs.",

keywords = "Infinite graphs, Laplace operator on graphs, Riemann-Roch theorem",

author = "Atsushi Atsuji and Hiroshi Kaneko",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2021",

doi = "10.1007/978-3-030-81976-7_9",

language = "English",

series = "STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics and Health",

publisher = "Springer Nature",

pages = "297--312",

booktitle = "STEAM-H",

address = "United States",

}