The asymptotic behavior of the average -discrepancies and a randomized discrepancy.
The Dispersion of the Hammersley Sequence in the Unit Square.
The inverse of the star-discrepancy depends linearly on the dimension
The k-functions in multiplicative number theory. III. Uniform distribution of zeta zeros; discrepancy
The k-functions in multiplicative number theory. IV. On a method of A. E. Ingham
The mantissa distribution of the primorial numbers
We show that the sequence of mantissas of the primorial numbers Pₙ, defined as the product of the first n prime numbers, is distributed following Benford's law. This is done by proving that the values of the first Chebyshev function at prime numbers are uniformly distributed modulo 1. We provide a convergence rate estimate. We also briefly treat some other sequences defined in the same way as Pₙ.
The rational points close to a curve
The rational points close to a curve II
The rational points close to a curve III