Explicit Formulas for Generalized Fractal Strings

  • Michel L. Lapidus
  • Machiel van Frankenhuijsen
Part of the Springer Monographs in Mathematics book series (SMM)


In 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.


Error Term Explicit Formula Zeta Function Complex Dimension Counting Function 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Michel L. Lapidus
    • 1
  • Machiel van Frankenhuijsen
    • 2
  1. 1.Department of MathematicsUniversity of California, RiversideRiversideUSA
  2. 2.Department of MathematicsUtah Valley UniversityOremUSA

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