On the distribution of the van der Corput sequence in arbitrary base

A central limit theorem with explicit error bound, and a large deviation result are proved for a sequence of weakly dependent random variables of a special form. As a corollary, under certain conditions on the function (f:[0,1] rightarrow mathbb {R}) a central limit theorem and a large deviation result are obtained for the sum (sum _{n=0}^{N-1} f(x_n)), where (x_n) is the base b van der Corput sequence for an arbitrary integer (b ge 2). Similar results are also proved for the (L^p) discrepancy of the same sequence for (1 le p < infty ). The main methods used in the proofs are the Berry–Esseen theorem and Fourier analysis.