ROC of $\mathcal{Z}$-Transform and zeros

1. What is the ROC of z-transform of?
2. What is ROC of z-transform and Laplace transform?
3. Can ROC include zeros?

What is the ROC of z-transform of?

Region of convergence. The region of convergence (ROC) is the set of points in the complex plane for which the Z-transform summation converges.

What is ROC of z-transform and Laplace transform?

Region of Convergence (ROC) of Z-Transform

The set of points in z-plane for which the Z-transform of a discrete-time sequence x(n), i.e., X(z) converges is called the region of convergence (ROC) of X(z).

Can ROC include zeros?

When n2>0 there will be a z−1 term and thus the ROC will not include z=0. When n1<0 then the sum will be infinite and thus the ROC will not include |z|=∞. On the other hand, when n2≤0 then the ROC will include z=0, and when n1≥0 the ROC will include |z|=∞.