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On approximation by Lüroth series

Karma Dajani, Cor Kraaikamp (1996)

Journal de théorie des nombres de Bordeaux

Let x ∈ ] 0 , 1 ] and p n / q n , n ≥ 1 be its sequence of Lüroth Series convergents. Define the approximation coefficients θ n = θ n ( x ) by q n x - p n , n ≥ 1 . In [BBDK] the limiting distribution of the sequence ( θ n ) n ≥ 1 was obtained for a.e. x using the natural extension of the ergodic system underlying the Lüroth Series expansion. Here we show that this can be done without the natural extension. In fact we will prove that for each n , θ n is already distributed according to the limiting distribution. Using the natural extension we will study the distribution for...

On Baker type lower bounds for linear forms

Tapani Matala-aho (2016)

Acta Arithmetica

A criterion is given for studying (explicit) Baker type lower bounds of linear forms in numbers 1 , Θ 1 , . . . , Θ m ∈ ℂ * over the ring ℤ of an imaginary quadratic field . This work deals with the simultaneous auxiliary functions case.

On Dyson's lemma

Carlo Viola (1985)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On gaps in Rényi β -expansions of unity for β > 1 an algebraic number

Jean-Louis Verger-Gaugry (2006)

Annales de l’institut Fourier

Let β > 1 be an algebraic number. We study the strings of zeros (“gaps”) in the Rényi β -expansion   d β ( 1 ) of unity which controls the set ℤ β of β -integers. Using a version of Liouville’s inequality which extends Mahler’s and Güting’s approximation theorems, the strings of zeros in d β ( 1 ) are shown to exhibit a “gappiness” asymptotically bounded above by   log ( M ( β ) ) / log ( β ) , where   M ( β )   is the Mahler measure of   β . The proof of this result provides in a natural way a new classification of algebraic numbers > 1 with classes called Q...

Currently displaying 801 – 820 of 1536