The Geometry of p-Adic Fractal Strings: A Comparative Survey

zbMath1276.37053arXiv1105.2966MaRDI QIDQ3100072

Michel L. Lapidus, Lũ' Hùng

Publication date: 22 November 2011

Full work available at URL: https://arxiv.org/abs/1105.2966

zbMATH Keywords

geometryharmonic analysisspectral theoryvolume formulatubular neighbourhoodcomplex dimension\(p\)-adic fractal stringsCantor string

Mathematics Subject Classification ID

Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Other Dirichlet series and zeta functions (11M41) Fractals (28A80) Continuous, (p)-adic and abstract analogues (11K41) Dynamical systems over non-Archimedean local ground fields (37P20) Alternative quantum mechanics (including hidden variables, etc.) (81Q65)

Related Items (8)

Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis ⋮ Truncated infinitesimal shifts, spectral operators and quantized universality of the Riemann zeta function ⋮ Distance and tube zeta functions of fractals and arbitrary compact sets ⋮ Fractal zeta functions and complex dimensions of relative fractal drums ⋮ Self-similar \(p\)-adic fractal strings and their complex dimensions ⋮ Fractal Zeta Functions and Complex Dimensions: A General Higher-Dimensional Theory ⋮ \(p\)-adic fractal strings of arbitrary rational dimensions and Cantor strings ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back

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