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We consider the recently introduced model of low ply graph drawing, a straight-line drawing in which the ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The ply-disk of a vertex is the disk centered at it whose radius is half the length of its longest incident edge. We focus our… (More)
In this paper we give irrationality results for numbers of the form ∑∞ n=1 an n! where the numbers an behave like a geometric progression for a while. The method is elementary, not using differentiation or integration. In particular, we derive elementary proofs of the irrationality of π and em for Gaussian integers m 6= 0.
In this paper we study the (ir)rationality of sums ∞
There are not many new results concerning the linear independence of numbers. Exceptions in the last decade are, e.g., the result of Sorokin  which proves the linear independence of logarithmus of special rational numbers, or that of Bezivin  which proves linear independence of roots of special functional equations. The algebraic independence of… (More)
© Université Bordeaux 1, 1996, tous droits réservés. L’accès aux archives de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.cedram.org/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale.… (More)
Using an idea of Erdős the paper establishes a criterion for the linear independence of infinite products which consist of rational numbers. A criterion for irrationality is obtained as a consequence.
Let f(n) or the base-2 logarithm of f(n) be either d(n) (the divisor function), σ(n) (the divisor-sum function), φ(n) (the Euler totient function), ω(n) (the number of distinct prime factors of n) or Ω(n) (the total number of prime factors of n). We present good lower bounds for ∣ ∣M N − α ∣ ∣ in terms of N , where α = [0; f(1), f(2), . . .].