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/(2π)), and complex numbers ν0=0,νn=nq+iαlog|nq|,|n|⩾1, the exponential system {tkeitνn:k=0,1,…,q−1}n=−∞∞ has excess 0 in L2(−π,π).