Rational approximations of . (Rationale Approximationen von .)
Rational approximations to and other algebraic numbers revisited
In this paper, we establish improved effective irrationality measures for certain numbers of the form , using approximations obtained from hypergeometric functions. These results are very close to the best possible using this method. We are able to obtain these results by determining very precise arithmetic information about the denominators of the coefficients of these hypergeometric functions.Improved bounds for the Chebyshev functions in arithmetic progressions and for are also presented....
Rational approximations to algebraic Laurent series with coefficients in a finite field
We give a general upper bound for the irrationality exponent of algebraic Laurent series with coefficients in a finite field. Our proof is based on a method introduced in a different framework by Adamczewski and Cassaigne. It makes use of automata theory and, in our context, of a classical theorem due to Christol. We then introduce a new approach which allows us to strongly improve this general bound in many cases. As an illustration, we give a few examples of algebraic Laurent series for which...
Rational approximations to linear forms in values of G-functions
Rational approximations to Tasoev continued fractions.
Rational approximations to the Rogers-Ramanujan continued fraction
Rational approximations to π and some other numbers
Rational points on a subanalytic surface
Let be a compact subanalytic surface. This paper shows that, in a suitable sense, there are very few rational points of that do not lie on some connected semialgebraic curve contained in .
Rational points on compact subgroups of algebraic groups. (Points rationnels sur les sous-groupes compacts des groupes algébriques.)
Rational points on the unit sphere
It is known that the unit sphere, centered at the origin in ℝn, has a dense set of points with rational coordinates. We give an elementary proof of this fact that includes explicit bounds on the complexity of the coordinates: for every point ν on the unit sphere in ℝn, and every ν > 0; there is a point r = (r 1; r 2;…;r n) such that: ⊎ ‖r-v‖∞ < ε.⊎ r is also a point on the unit sphere; Σ r i 2 = 1.⊎ r has rational coordinates; for some integers a i, b i.⊎ for all . One consequence of this...
Rational values of the arccosine function
We give a short proof to characterize the cases when arccos(√r), the arccosine of the squareroot of a rational number r ∈ [0, 1], is a rational multiple of π: This happens exactly if r is an integer multiple of 1/4. The proof relies on the well-known recurrence relation for the Chebyshev polynomials of the first kind.
Rationale Approximationen am Einheitskreis.
Rationale Punkte über eine algebraische Kurve (points rationnels sur une courbe algébrique)
Rauzy tilings and bounded remainder sets on the torus.
Recipes for Solving Diophantine Problems by Baker's Method
Recouvrement optimal du cercle par les multiples d'un intervalle
Récurrences - et -mahlériennes
On sait (Cobham) qu’une suite - et -automatique est une suite rationnelle. Une question de Loxton et van der Poorten étend ce résultat au cas - et -régulier. On montre dans cet article que, si une suite vérifie une récurrence - et -mahlérienne d’ordre un, elle est rationnelle.
Regularity of distribution of (nα)-sequences
Relations de dépendance linéaire entre des logarithmes de nombres algébriques
Remark on periodic solutions of a linear wave equation in one dimension