  Wigner limits are given formally as the difference between a lattice sum,
associated to a positive definite quadratic form, and a corresponding multiple
integral. To define these limits, which arose in work of Wigner on the energy
of static electron lattices, in a mathematically rigorous way one commonly
truncates the lattice sum and the corresponding integral and takes the limit
along expanding hypercubes or other regular geometric shapes. We generalize the
known mathematically rigorous two and three dimensional results regarding
Wigner limits, as laid down in [Analysis of certain lattice sums, D. Borwein,
J. M. Borwein, and R. Shail, 1989], to integer lattices of arbitrary dimension.
In doing so, we also resolve a problem posed in Chapter 7 of [Lattice Sums:
Then and Now, J. M. Borwein, L. Glasser, R. McPhedran, J. G. Wan, and I. J.
Zucker, 2013].
  For the sake of clarity, we begin by considering the simpler case of cubic
lattice sums first, before treating the case of arbitrary quadratic forms. We
also consider limits taken along expanding hyperballs with respect to general
norms, and connect with classical topics such as Gauss's circle problem. An
appendix is included to recall certain properties of Epstein zeta functions
that are either used in the paper or serve to provide perspective.
