  Motivated by the study of spectral properties of self-adjoint operators in
the integral group ring of a sofic group, we define and study integer
operators. We establish a relation with classical potential theory and in
particular the circle of results obtained by M. Fekete and G. Szeg"o. More
concretely, we use results by R. Rumely on equidistribution of algebraic
integers to obtain a description of those integer operator which have spectrum
of logarithmic capacity less or equal to one.
  Finally, we relate the study of integer operators to a recent construction by
B. and L. Petracovici and A. Zaharescu.
