A distance measure on finite abelian groups and an application to quasi-Monte Carlo integration (Q1272190)

The author studies, for two finite abelian groups \(G\), \(H\) and a mapping (maybe not a homomorphism) \(f\) between them, the matrix whose \((r,s)\)-entry is the inner product of \(r(f)\) and \(s\), where \(r\), \(s\) are complex characters of \(G\), \(H\). From this he defines a metric on the space of finite abelian groups of order \(n\) and gives a theorem estimating character sums on \(m\) fold products of the group. He uses this in turn to give estimates on the error involved in quasi-Monte Carlo numerical integration using digital \((t,m,s)\)-nets.