The zeta-dimension of a set A of positive integers is the infimum s such that the sum of the reciprocals of the s-th powers of the elements of A is finite.
Mar 22, 2005
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Zeta-dimension serves as a fractal dimension on Z+ that extends naturally and usefully to discrete lattices such as Zd, where d is a positive integer.
Zeta-dimension serves as a fractal dimension on ℤ + that extends naturally and usefully to discrete lattices such as ℤd, where d is a positive integer.
The zeta-dimension of a set A of positive integers is Dimζ (A) = inf{s | ζ A (s) < ∞ }, where \(\zeta_A(s)=\sum_{n\in A}n^{-s}.\) Zeta-dimension serves as a ...
Zeta-dimension serves as a fractal dimension on Z+ that extends natu- rally and usefully to discrete lattices such as Zd, where d is a positive integer.
Zeta-dimension serves as a fractal dimension on ℤ+ that extends naturally ... These fractal dimensions are called upper zeta dimension and lower…
May 30, 2018 · to define the dimension of a network. Download chapter PDF. In this final chapter we consider the use of the zeta function.
Mar 22, 2005 · Zeta-dimension serves as a fractal dimension on Z+ that extends naturally and usefully to discrete lattices such as Zd, ...
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Feb 24, 2018 · These fractal dimensions are called upper zeta dimension and lower zeta dimension. The upper zeta dimension is an extension of the zeta ...