On the beta-expansions of 1 and algebraic numbers for a Salem number beta-Reference-Cited by-同舟云学术

On the beta-expansions of 1 and algebraic numbers for a Salem number beta

Published:2014-02-26 Issue:4 Volume:35 Page:1243-1262
ISSN:0143-3857
Container-title:Ergodic Theory and Dynamical Systems
language:en
Short-container-title:Ergod. Th. Dynam. Sys.

Author:

KANEKO HAJIME

Abstract

AbstractWe study the digits of

$\beta $

-expansions in the case where

$\beta $

is a Salem number. We introduce new upper bounds for the numbers of occurrences of consecutive 0s in the expansion of 1. We also give lower bounds for the numbers of non-zero digits in the

$\beta $

-expansions of algebraic numbers. As applications, we give criteria for transcendence of the values of power series at certain algebraic points.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,General Mathematics

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