The lead digit behavior of a large class of arithmetic sequences is determined by using results from the theory of uniform distribution $\operatorname {mod} 1$. Theory for triangular arrays is ...

If X = (X1, ⋯, Xn) has uniform distribution on the sphere or ball in Rn with radius a, then the joint distribution of n1/2a-1 Xi, i = 1, ⋯, k, converges in total variation to the standard normal ...