Abstract
We investigate the existence of the meromorphic extension of the spectral zeta function of a Laplacian on self-similar fractals using the results of Kigami and Lapidus (based on renewal theory) and the newer results by Hambly and Kajino based on heat kernel estimates and other probabilistic techniques. We also formulate conjectures which hold true for the examples that have been analyzed in the existing literature.
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Research supported in part by the National Science Foundation, grants DMS-0652440 (first author) and DMS-0505622 (second author).
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Steinhurst, B.A., Teplyaev, A. Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals. Lett Math Phys 103, 1377–1388 (2013). https://doi.org/10.1007/s11005-013-0649-y
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DOI: https://doi.org/10.1007/s11005-013-0649-y