Continued fractions of Laurent series with partial quotients from a given set
Continued Fractions of Transcendental Numbers
Continued fractions on the Heisenberg group
We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions.
Contributions to Diophantine Approximation in Fields of Series.
Contributions to the theory of transcendental numbers (I)
Contributions to the theory of transcendental numbers (II)
Convergence of Continued Fraction Type Algorithms and Generators.
Convergents and irrationality measures of logarithms.
Convergents of folded continued fractions
Correct rounding of algebraic functions
We explicit the link between the computer arithmetic problem of providing correctly rounded algebraic functions and some diophantine approximation issues. This allows to get bounds on the accuracy with which intermediate calculations must be performed to correctly round these functions.
Correction to : “Linear fractional transformations of continued fractions with bounded partial quotients”
We fill a gap in the proof of a theorem of our paper cited in the title.
Correction to my paper: Arithmetic properties of certain power series with algebraic coefficents
Correction to the paper "Divergent trajectories of flows on homogeneous spaces and Diophantine approximations".
Corrections to “How to explicitly solve a Thue-Mahler equation”
Corrigenda: ‘On systems of linear inequalities’
There are two mistakes in the referred paper. One is ridiculous and one is significant. But none is serious.
Corrigendum to "On density modulo 1 of some expressions containing algebraic integers" (Acta Arith. 127 (2007), 217-229)
Corrigendum to the paper "Constants for lower bounds for linear forms in the logarithms of algebraic numbers II. The homogeneous rational case" (Acta Arith. 55 (1990), 15-22)
Counting invertible matrices and uniform distribution
Consider the group over the ring of algebraic integers of a number field . Define the height of a matrix to be the maximum over all the conjugates of its entries in absolute value. Let be the number of matrices in with height bounded by . We determine the asymptotic behaviour of as goes to infinity including an error term,with being the degree of . The constant involves the discriminant of , an integral depending only on the signature of , and the value of the Dedekind zeta function...
Counting problems and semisimple groups.
Counting rational points near planar curves
We find an asymptotic formula for the number of rational points near planar curves. More precisely, if f:ℝ → ℝ is a sufficiently smooth function defined on the interval [η,ξ], then the number of rational points with denominator no larger than Q that lie within a δ-neighborhood of the graph of f is shown to be asymptotically equivalent to (ξ-η)δQ².