In this article, we study the interlacing property of the weakly holomorphic Poincaré series \(G_k(z,-m)\) on the unit circle, for integers \(m \ge 1\) and \(k \ge 4\) . The second author and Saradha established the interlacing property of the zeros of \(G_k(z,-m)\) and \(G_{k+12}(z,-m)\) on the restricted arc \(A_\epsilon :=\{e^{i \theta }: \theta \in (\pi /2,2\pi /3-\epsilon )\}\) for any \(0<\epsilon <\pi /6\) for (explicitly computable) large k depending upon m and \(\epsilon \) . They also established a similar interlacing property of the zeros of \(G_k(z,-m)\) and \(G_k(z,-m-1)\) on \(A_\epsilon \) for (explicitly computable) large m depending upon k and \(\epsilon \) . However, such restricted interlacing fails to treat a positive proportion of the zeros. To complete their work, in this article, we show that the zeros of \(G_k(z,-m)\) , \(G_{k+12}(z,-m)\) interlace on the whole open arc \(A^\circ :=\{e^{i \theta }: \theta \in (\pi /2,2\pi /3)\}\) . With some additional effort, we are also able to show that the zeros of \(G_k(z,-m)\) , \(G_{k}(z,-m-1)\) interlace on the arc \(A^\circ \) .
