  The $\boldsymbol{p}$-adic diaphony as introduced by Hellekalek is a
quantitative measure for the irregularity of distribution of a sequence in the
unit cube. In this paper we show how this notion of diaphony can be interpreted
as worst-case integration error in a certain reproducing kernel Hilbert space.
Our main result is an upper bound on the $\boldsymbol{p}$-adic diaphony of the
Halton sequence.

Number Theory