Knot Complement Problem for L-space $\mathbb{Z}H{S}^3$

In this paper we look at the knot complement problem for L-space $\mathbb{Z}$-homology spheres. We show that an L-space $\mathbb{Z}$-homology sphere $Y$ cannot be obtained as a non-trivial surgery along a knot $K\subset Y$\mathrm{.}Asaconsequence,weprovethatknotsinanL-space$$\mathbb{Z}$$-homology sphere are determined by their complements.