Explicit Formulas for Generalized Fractal Strings

Michel L. Lapidus () and Machiel van Frankenhuysen ()
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Michel L. Lapidus: University of California, Department of Mathematics
Machiel van Frankenhuysen: University of California, Department of Mathematics

Chapter 4 in Fractal Geometry and Number Theory, 2000, pp 71-109 from Springer

Abstract: Abstract In this chapter, we present our (pointwise and distributional) explicit formulas for the lengths and frequencies of a fractal string. To unify the exposition, and with a view toward later applications, we formulate our results in the language of generalized fractal strings, introduced in Chapter 3. The explicit formulas express the counting function of the lengths or of the frequencies as a sum over the visible complex dimensions ω of the generalized fractal string η.

Keywords: Error Term; Explicit Formula; Zeta Function; Complex Dimension; Counting Function (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-5314-3_5

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DOI: 10.1007/978-1-4612-5314-3_5

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