The distribution of rational points close to a smooth manifold and Hausdorff dimension
The distribution of sequences modulo one
The divisors of integers I
The divisors of integers II
The Farey Series of polynomials over a finite field.
The Fermat equation with polynomial values as base variables.
The Fractional Parts of a Sum of Polynomials.
The geometry of badly approximable vectors.
The greatest prime factor of
The group structure for ζ(3)
The Hausdorff dimension of certain sets arising from Diophantine approximation by restricted sequences of integer vectors
The Hausdorff dimension of sets arising in metric Diophantine approximation
The Hausdorff dimension of systems of linear forms
The hyperbolic geometry of continued fractions .
The integer Chebyshev constant of Farey intervals.
We obtain new bounds for the integer Chebyshev constant of intervals [p/q, r/s] where p, q, r and s are non-negative integers such that qr - ps = 1. As a consequence of the methods used, we improve the known lower bound for the trace of totally positive algebraic integers.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
The irrationality of some number theoretical series
The Jacobi-Perron Algorithm and Pisot numbers
The -dimensional Duffin and Schaeffer conjecture
We show that the Duffin and Schaeffer conjecture holds in all dimensions greater than one.
The Lagrange spectrum of a set
The Lagrange theorem for multidimensional diophantine approximation.