On multiplier systems and theta functions of half-integral weight for the Hilbert modular group ${\mathrm{SL}}_2(\mathfrak{o})$

Hiroshi Noguchi

Let $F$ be a totally real number field and $\mathfrak{o}$ the ring of integers of $F$. We study theta functions which are Hilbert modular forms of half-integral weight for the Hilb…