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 $\RR/\ZZ$.
Optimal and typical $L^2$ discrepancy of 2-dimensional lattices
On the lower bound of the discrepancy of $(t,s)$ sequences: II
On the upper bound of the $L_2$-discrepancy of Halton's sequence
![QR code for arXiv:1904.01714 [math.NT]](http://oss.arxitics.com/images/favicon.svg)