Distance and tube zeta functions of fractals and arbitrary compact sets

DOI10.1016/j.aim.2016.11.034zbMath1367.28004arXiv1506.03525OpenAlexW573702276MaRDI QIDQ502674

Michel L. Lapidus, Darko Žubrinić, Goran Radunović

Publication date: 5 January 2017

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.03525

zbMATH Keywords

zeta functionbox dimensionfractal setMinkowski contentresiduecomplex dimensionsDirichlet-type integraldistance zeta functionfractal stringfractality and complex dimensionsMinkowski measurable setprincipal complex dimensionstranscendentally quasiperiodic settube zeta function

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Fractals (28A80)

Related Items (9)

Maximally singular weak solutions of Laplace equations ⋮ Complex dimensions of fractals and meromorphic extensions of fractal zeta functions ⋮ Fractal zeta functions of orbits of parabolic diffeomorphisms ⋮ \(h\)-Laplacians on singular sets ⋮ Quasiperiodic sets at infinity and meromorphic extensions of their fractal zeta functions ⋮ Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces ⋮ Fractal zeta functions and complex dimensions of relative fractal drums ⋮ Fractal Zeta Functions and Complex Dimensions: A General Higher-Dimensional Theory ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back

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