On the excess of complex exponential systems in L²(-a,a)

In this article we give new criteria for two complex sequences to have the same excess in the sense of Paley and Wiener in L² (-a, a). As a result, we prove that given any positive integer q, a real number α ∈ (0, 1/(2 π)), and complex numbers ν₀, ν_n = nq + i α log nq , n ≥ 1, the exponential system {t^k e^itνn: k = 0, 1,...,q - 1}_n=-∞^∞ has excess 0 in L² (-π, π).