  We derive an inequality on the discrepancy of sequences on the ring of
$p$-adic integers $\ZZ_p$ using techniques from Fourier analysis. The
inequality is used to obtain an upper bound on the discrepancy of the sequence
$\alpha_n = na +b$, where $a$ and $b$ are elements of $\ZZ_p$. This is a
$p$-adic analogue of the classical LeVeque inequality on the circle group
$\RR/\ZZ$.
