characteristics of the strata yields $$Z^{mon}_{Y,0}(t) = \frac{\prod\limits_{k = 0}^g(1-t^{M_k})^{\frac{{\bar{\beta}}_k}{M_k}}}{\prod\limits_{k = 1}^g(1-t^{N_k})^{\frac{n_k{\bar{\beta}}_k}{N_k}}},$$ where $$M_k := \operatorname{lcm}\Big(\frac{{\bar{\beta}}_k}{\gcd({\bar{\beta}}_0,\ldots, {\bar{\beta}}_k)},n_{k+1},\ldots, n_g\Big), \quad k = 0,\ldots, g,$$ and $$N_k := \operatorname{lcm}\Big(\frac{{\bar{\beta}}_k}{\gcd({\bar{\beta}}_0,\ldots, {\bar{\beta}}_k)},n_k,\ldots, n_g\Big), \quad k = 1,\ldots, g.$$ It follows that the monodromy zeta function $Z_{Y,p}^{mon}(t)$ of $Y \subset {\mathbb C}^{g+1}$ at $p = S' \cap \sigma^{-1}(0)$ is given by the same expression, see Theorem \[thm:zeta-function-mon-Y\].

With this expression for $Z_{Y,p}^{mon}(t)$, we will be able to prove the monodromy conjecture for a space monomial curve $Y \subset {\mathbb C}^{g+1}$. More precisely, we will show in Theorem \[thm:mon-conj\] that every pole ${\mathbb L}^{-s_0}$ of the motivic Igusa zeta function associated with $Y$ yields a monodromy eigenvalue $e^{2\pi is_0}$ of $Y$. We will see that the poles ${\mathbb L}^{g}$ and ${\mathbb L}^{\frac{\nu_k}{N_k}}$ with $\frac{\nu_k}{N_k} \in {\mathbb N}$ induce the trivial monodromy eigenvalue $1$, being a zero of the monodromy zeta function at any point in $E' \setminus \sigma^{-1}(0)$. For the other poles ${\mathbb L}^{\frac{\nu_k}{N_k}}$ with $\frac{\nu_k}{N_k} \notin {\mathbb N}$, we will prove that the candidate monodromy eigenvalue $e^{-2\pi i\frac{\nu_k}{N_k}}$ is a pole of $Z^{mon}_{Y,p}(t)$.

This article consists of the following sections. Section \[SpaceMonomial\] introduces the monomial curves $Y \subset {\mathbb C}^{g+1}$ of our interest. In Section 