Zeta functions of discrete self-similar sets. - Archive ouverte HAL
Article Dans Une Revue Advances in Mathematics Année : 2013

Zeta functions of discrete self-similar sets.

Driss Essouabri
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Ben Lichtin
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Résumé

In 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.

Dates et versions

hal-00947521 , version 1 (16-02-2014)

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Driss Essouabri, Ben Lichtin. Zeta functions of discrete self-similar sets.. Advances in Mathematics, 2013, 232, pp.142-187. ⟨10.1016/j.aim.2012.09.011⟩. ⟨hal-00947521⟩
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