Let
${\vartheta}_{3}\left(\tau \right)=1+2{\sum}_{\nu =1}^{\infty}{e}^{\pi i{\nu}^{2}\tau}$
denote the classical Jacobi thetaconstant. We prove that the two values
${\vartheta}_{3}\left(m\tau \right)$ and
${\vartheta}_{3}\left(n\tau \right)$ are algebraically
independent over
$\mathbb{Q}$
for any
$\tau $ in the upper
halfplane such that
$q={e}^{\pi i\tau}$ is an
algebraic number, where
$m,n\ge 2$
are distinct integers.
