Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractal zeta functions and complex dimensions: A general
  higher-dimensional theory   In 2009, the first author introduced a class of zeta functions, called
`distance zeta functions', which has enabled us to extend the existing theory
of zeta functions of fractal strings and sprays (initiated by the first author
and his collaborators in the early 1990s) to arbitrary bounded (fractal) sets
in Euclidean spaces of any dimensions. A closely related tool is the class of
`tube zeta functions', defined using the tube function of a fractal set. These
zeta functions exhibit deep connections with Minkowski contents and upper box
(or Minkowski) dimensions, as well as, more generally, with the complex
dimensions of fractal sets. In particular, the abscissa of (Lebesgue, i.e.,
absolute) convergence of the distance zeta function coincides with the upper
box dimension of a set. We also introduce a class of transcendentally
quasiperiodic sets, and describe their construction based on a sequence of
carefully chosen generalized Cantor sets with two auxilliary parameters. As a
result, we obtain a family of "maximally hyperfractal" compact sets and
relative fractal drums (i.e., such that the associated fractal zeta functions
have a singularity at every point of the critical line of convergence).
Finally, we discuss the general fractal tube formulas and the Minkowski
measurability criterion obtained by the authors in the context of relative
fractal drums (and, in particular, of bounded subsets of the N-dimensional
Euclidean space).

15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn