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Fractality and Lapidus zeta functions at infinity

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arxiv 1510.06449 v2 pith:P2FFSXXE submitted 2015-10-21 math-ph math.MP

Goran Radunović (University of Zagreb) This is my paper · ORCID
classification math-phmath.MP
keywords infinityfractalitylapiduspropertiessetsunboundedzetaanalysis
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We study fractality of unbounded sets of finite Lebesgue measure at infinity by introducing the notions of Minkowski dimension and content at infinity. We also introduce the Lapidus zeta function at infinity, study its properties and demonstrate its use in analysis of fractal properties of unbounded sets at infinity.

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  1. Essential singularities of fractal zeta functions

    math-ph 2019-08 conditional novelty 6.0 of 10

    For any three numbers D_inf < D_1 <= D in [0,1], the authors construct a bounded fractal string whose zeta function has paramorphic barrier D_inf, meromorphic abscissa D_1, and absolute convergence abscissa D.

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