  In this paper we introduce an interesting family of relative fractal drums
(RFDs in short) at infinity and study their complex dimensions which are
defined as the poles of their associated Lapidus (distance) fractal zeta
functions introduced in a previous work by the author.
  We define the tube zeta function at infinity and obtain a functional equation
connecting it to the distance zeta function at infinity much as in the
classical setting. Furthermore, under suitable assumptions, we provide general
results about existence of meromorphic extensions of fractal zeta functions at
infinity in the Minkowski measurable and nonmeasurable case. We also provide a
sufficiency condition for Minkowski measurability as well as an upper bound for
the upper Minkowski content, both in terms of the complex dimensions of the
associated RFD.
  We show that complex dimensions of quasiperiodic sets at infinity posses a
quasiperiodic structure which can be either algebraic or transcedental.
Furthermore, we provide an example of a maximally hyperfractal set at infinity
with prescribed Minkowski dimension, i.e., a set such that the abscissa of
convergence of the corresponding fractal zeta function is in fact its natural
boundary.
