  Consider the solution $\mathcal{Z}(t,x)$ of the one-dimensional stochastic
heat equation, with a multiplicative spacetime white noise, and with the delta
initial data $\mathcal{Z}(0,x) = \delta(x)$. For any real $p>0$, we obtained
detailed estimates of the $p$-th moment of $e^{t/12}\mathcal{Z}(2t,0)$, as
$t\to\infty$, and from these estimates establish the one-point upper-tail large
deviation principle of the Kardar-Parisi-Zhang equation. The deviations have
speed $t$ and rate function $\Phi_+(y)=\frac{4}{3}y^{3/2}$. Our result confirms
the existing physics predictions [Le Doussal, Majumdar, Schehr 16] and also
[Kamenev, Meerson, Sasorov 16].
