The Lagrange theorem for multidimensional diophantine approximation.
The localisation of primes in arithmetic progressions of irrational modulus
A new method for counting primes in a Beatty sequence is proposed, and it is shown that an asymptotic formula can be obtained for the number of such primes in a short interval.
The lonely runner with seven runners.
The Markoff spectrum
The metric simultaneous diophantine approximations over formal power series
We discuss the metric theory of simultaneous diophantine approximations in the non-archimedean case. First, we show a Gallagher type 0-1 law. Then by using this theorem, we prove a Duffin-Schaeffer type theorem.
The metrical theory of continued fractions to the nearer integer
The Modular Symbol and Continued Fractions in Higher Dimensions.
The Number of Steps in a Finite Jacobi Algorithm.
The number of subspaces occurring in the p-adic subspace theorem in diophantine approximation.
The √p Riemann surface
The permutation group method for the dilogarithm
We give qualitative and quantitative improvements on all the best previously known irrationality results for dilogarithms of positive rational numbers. We obtain such improvements by applying our permutation group method to the diophantine study of double integrals of rational functions related to the dilogarithm.
The plank problem for symmetric bodies.
The polylogarithm in the field of two irreducible quintics.
The Quality of the Diophantine Approximations Found by the Jacobi-Perron Algorithm and Related Algorithms.
The quantitative subspace theorem for number fields
The rational points close to a curve
The rational points close to a curve II
The rational points close to a curve III
The Rhin-Viola method for log 2
The role of the Lagrange constant in some nonlinear waves equations.