Badly Approximable Formal Power Series.
Badly approximable systems of linear forms over a field of formal series
We prove that the Hausdorff dimension of the set of badly approximable systems of linear forms in variables over the field of Laurent series with coefficients from a finite field is maximal. This is an analogue of Schmidt’s multi-dimensional generalisation of Jarník’s Theorem on badly approximable numbers.
Bad(s,t) is hyperplane absolute winning
J. An proved that for any s,t ≥ 0 such that s + t = 1, Bad (s,t) is (34√2)¯¹-winning for Schmidt's game. We show that using the main lemma from [An] one can derive a stronger result, namely that Bad (s,t) is hyperplane absolute winning in the sense of [BFKRW]. As a consequence, one can deduce the full Hausdorff dimension of Bad (s,t) intersected with certain fractals.
Beatty sequences and multiplicative number theory
Bemerkung über irrationale Zahlen
Bemerkungen über Kettenbrüche.
Bemerkungen zu einem Approximationssatz für regelmäßige Kettenbrüche.
Best diophantine approximations for ternary linear forms.
Best simultaneous diophantine approximations of Pisot numbers and Rauzy fractals
Best simultaneous diophantine approximations of some cubic algebraic numbers
Let be a real algebraic number of degree over whose conjugates are not real. There exists an unit of the ring of integer of for which it is possible to describe the set of all best approximation vectors of .’
Beukers' integrals and Apéry's recurrences.
Beweis der Transcendenz der Zahl e.
Beweis der Transcendenz der Zahl e
Billiard and diophantine approximation
Billiards and the five distance theorem
Birational transformations and values of the Riemann zeta-function
In his proof of Apery’s theorem on the irrationality of , Beukers [B] introduced double and triple integrals of suitable rational functions yielding good sequences of rational approximations to and . Beukers’ method was subsequently improved by Dvornicich and Viola, by Hata, and by Rhin and Viola. We give here a survey of our recent results ([RV2] and [RV3]) on the irrationality measures of and based upon a new algebraic method involving birational transformations and permutation groups...
Bounded discrepancy sets
Bounding squares in second order recurrence sequences
Bounds for the solutions of S-unit equations and decomposable form equations
Bounds for the solutions of Thue-Mahler equations and norm form equations