6533b7d5fe1ef96bd12647a7

RESEARCH PRODUCT

Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets

Boris SolomyakPablo Shmerkin

subject

Power seriesDiscrete mathematics28A80Social connectednessGeneral Mathematics010102 general mathematics01 natural sciencesSet (abstract data type)Bernoulli's principleFractal30C1528A80 30B10Mathematics - Classical Analysis and ODEs0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: Mathematicsself-affine fractals010307 mathematical physicsAffine transformationZeros of power series0101 mathematicsMathematics

description

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

yearjournalcountryeditionlanguage
2006-01-01
https://dx.doi.org/10.48550/arxiv.math/0504545