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Displaying 361 –
380 of
906
We study the complexity of the infinite word associated with the Rényi expansion of in an irrational base . When is the golden ratio, this is the well known Fibonacci word, which is sturmian, and of complexity . For such that is finite we provide a simple description of the structure of special factors of the word . When we show that . In the cases when or we show that the first difference of the complexity function takes value in for every , and consequently we determine...
We study the complexity of the infinite word uβ associated with the
Rényi expansion of 1 in an irrational base β > 1.
When β is the golden ratio, this is the well known Fibonacci word,
which is Sturmian, and of complexity C(n) = n + 1.
For β such that
dβ(1) = t1t2...tm is finite we provide a simple description of
the structure of special factors of the word uβ. When tm=1
we show that
C(n) = (m - 1)n + 1. In the cases when t1 = t2 = ... tm-1or
t1 > max{t2,...,tm-1} we show that the first difference
of...
Le terme principal de la moyenne, sur les discriminants quadratiques satisfaisant la condition de Heegner, de la hauteur de Néron-Tate des points de Heegner d’une courbe elliptique rationnelle a été déterminé dans [13]. Les auteurs ont également conjecturé l’expression du terme suivant. Dans cet article, il est démontré que cette expression est correcte et une asymptotique précise, qui sauve une puissance dans le terme d’erreur, est obtenue. Les annulations des coefficients de Fourier de formes...
We describe the average behaviour of the Brjuno function Φ in the neighbourhood of any given point of the unit interval. In particular, we show that the Lebesgue set of Φ is the set of Brjuno numbers and we find the asymptotic behaviour of the modulus of continuity of the integral of Φ.
In this note, we show that the counting function of the number of composite positive integers such that is a prime is of order of magnitude at least and at most .
We consider a rational function which is ‘lacunary’ in the sense that it can be expressed as the ratio of two polynomials (not necessarily coprime) having each at most a given number of terms. Then we look at the possible decompositions , where are rational functions of degree larger than 1. We prove that, apart from certain exceptional cases which we completely describe, the degree of is bounded only in terms of (and we provide explicit bounds). This supports and quantifies the intuitive...
Currently displaying 361 –
380 of
906