Sets of block structure and discrepancy estimates
Some Distribution Properties of 0,1-Sequences.
Some remarks on the discrepancy of the sequence
Some remarks on the distribution of a sequence connected with .
Some upper bounds in the theory of irregularities of distribution
Substitutions and 1/2-discrepancy of nθ + x
Suites dont discrépance est comparable à un logarithme.
Sums of distances between points of a sphere.
Sums of distances to the nearest integer and the discrepancy of digital nets
Sur les discrépances
Symbolic discrepancy and self-similar dynamics
We consider subshifts arising from primitive substitutions, which are known to be uniquely ergodic dynamical systems. In order to precise this point, we introduce a symbolic notion of discrepancy. We show how the distribution of such a subshift is in part ruled by the spectrum of the incidence matrices associated with the underlying substitution. We also give some applications of these results in connection with the spectral study of substitutive dynamical systems.
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