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2006 Zeros of $\{-1,0,1\}$ Power Series and Connectedness Loci for Self-Affine Sets
Pablo Shmerkin, Boris Solomyak
Experiment. Math. 15(4): 499-511 (2006).

Abstract

We consider the set $\Om_2$ of double zeros in $(0,1)$ for power series with coefficients in $\{-1,0,1\}$. We prove that $\Om_2$ is disconnected, and estimate $\min \Om_2$ with high accuracy. We also show that $[2^{-1/2}-\eta,1)\subset \Om_2$ for some small, but explicit, $\eta>0$ (this was known only for $\eta=0$). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine fractals.

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Pablo Shmerkin. Boris Solomyak. "Zeros of $\{-1,0,1\}$ Power Series and Connectedness Loci for Self-Affine Sets." Experiment. Math. 15 (4) 499 - 511, 2006.

Information

Published: 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1122.30002
MathSciNet: MR2293600

Subjects:
Primary: 30C15
Secondary: 28A80

Keywords: self-affine fractals , Zeros of power series

Rights: Copyright © 2006 A K Peters, Ltd.

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Vol.15 • No. 4 • 2006
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