On the irrationality of $\zeta(\frac{3}{2})$

Question

It is known that $$\zeta(s)=\sum_{n=1}^\infty\frac{1}{n^s}$$Where $\zeta$ is riemann's zeta function. Usually people make $s$ an integer. But I thought of non integer values of $s$ and started with $s=\frac32$. So I wondered if $\zeta(\frac32)$ is irrational. According to wolfram alpha, this is unknown. But is there any research on the irrationality/transcendence of this number?