On the Dirichlet series related to the cubic theta function

The paper studies the function $L(\tau;\cdot)$ defined by the Dirichlet series
$$ L(\tau;s)=\sum_\nu\frac{\tau(\nu)}{\|\nu\|^s}, \quad s\in\mathbb C, $$
where $\tau(\nu)$ is the $\nu$th Fourier coefficient of the Kubota?Patterson cubic theta function. For this function, an exact and an approximate functional equations are derived. It is established that the function does not vanish in the halfplane $\operatorname{RE}s\ge 1.3533$ and has no singularities except for a simple pole at the point 5/6. Issues related to computing the coefficients $\tau(\nu)$ and values of the special functions arising in the approximate functional equation are considered. Bibliography: 11 titles.