AbstractIn this paper we study a class of countable and discrete subsets of a Euclidean space that are “self-similar” with respect to a finite set of (affine) similarities. Any such set can be interpreted as having a fractal structure. We introduce a zeta function for these sets, and derive basic analytic properties of this “fractal” zeta function. Motivating examples that come from combinatorial geometry and arithmetic are given particular attention
Abstract. We discuss a number of techniques for determining the Minkowski dimension of bounded subse...
Topological behaviour of self-similar spectra for fractal domains is shown. Two different mathematic...
The recent field of analysis on fractals has been studied under a probabilistic and analytic point o...
46 pages.International audienceIn this paper we study a class of countable and discrete subsets of a...
In the first chapter we define and look at examples of self-similar sets and some of\ud their proper...
Visualization of sets in Euclidean space that possess notions of non-integer dimension has lead to a...
Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics I, Fractals in Pure Mathemati...
This paper solves the general Erdös-Szemeredi conjecture for some classes of increasing families of ...
International audienceThis paper solves the general Erdos-Szemeredi conjecture for some classes of i...
International audienceIn this paper we first prove analytical properties of zeta functions for discr...
International audienceThis paper uses the zeta function methods to solve Falconer-type problems abou...
Fractal zeta functions associated to bounded subsets of Euclidean spaces relate the geometry of a se...
We study the spectral zeta functions of the Laplacian on fractal sets which are locally self-similar...
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional...
Starting with Ihara's work in 1968, there has been a growing interest in the study of zeta functions...
Abstract. We discuss a number of techniques for determining the Minkowski dimension of bounded subse...
Topological behaviour of self-similar spectra for fractal domains is shown. Two different mathematic...
The recent field of analysis on fractals has been studied under a probabilistic and analytic point o...
46 pages.International audienceIn this paper we study a class of countable and discrete subsets of a...
In the first chapter we define and look at examples of self-similar sets and some of\ud their proper...
Visualization of sets in Euclidean space that possess notions of non-integer dimension has lead to a...
Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics I, Fractals in Pure Mathemati...
This paper solves the general Erdös-Szemeredi conjecture for some classes of increasing families of ...
International audienceThis paper solves the general Erdos-Szemeredi conjecture for some classes of i...
International audienceIn this paper we first prove analytical properties of zeta functions for discr...
International audienceThis paper uses the zeta function methods to solve Falconer-type problems abou...
Fractal zeta functions associated to bounded subsets of Euclidean spaces relate the geometry of a se...
We study the spectral zeta functions of the Laplacian on fractal sets which are locally self-similar...
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional...
Starting with Ihara's work in 1968, there has been a growing interest in the study of zeta functions...
Abstract. We discuss a number of techniques for determining the Minkowski dimension of bounded subse...
Topological behaviour of self-similar spectra for fractal domains is shown. Two different mathematic...
The recent field of analysis on fractals has been studied under a probabilistic and analytic point o...
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