The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Page 1

Displaying 1 – 20 of 20

Showing per page

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 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 1 – 20 of 20

Page 1