Explicit Formulas for Generalized Fractal Strings

Michel L Lapidus,Machiel Van Frankenhuijsen

doi:10.1007/978-1-4614-2176-4_5

Explicit Formulas for Generalized Fractal Strings

Michel L Lapidus, Machiel Van Frankenhuijsen

https://doi.org/10.1007/978-1-4614-2176-4_5

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Publication Date: Sep 2, 2012

Affiliation: University of California, Riverside, Utah Valley University

#Counting Functions #Explicit Formulas + Show 4 more

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Abstract

AbstractIn this chapter, we obtain pointwise and distributional explicit formulas for the counting functions of the lengths and of the frequencies of a fractal string. These explicit formulas express these counting functions as a sum over the visible complex dimensions W of the fractal string.KeywordsError TermExplicit FormulaZeta FunctionComplex DimensionCounting FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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