On covering equivalence

An arithmetic sequence a(n) = {a + nx : x is an element of Z} (0 less than or equal to a < n) with weight A G C is denoted by (A, a, n). For two finite systems A = {[lambda(s), a(s), n(s)]}(s=1)(k) and beta = {[mu(t), b(t), m(t)]}(t=1)(l) of such triples, if Sigma(ns\x - as) lambda(s) = Sigma(mt\x-bt) mu(t) for all x is an element of Z then we say that A and 8 are covering equivalent. In this paper we characterize covering equivalence in various ways, our characterizations involve the Gamma-function, the Hurwitz zeta-function, trigonometric functions, the greatest integer function and Egyptian fractions.