Zeros of (−1, 0, 1) power series and connectedness loci for self-affine sets

Pablo Shmerkin, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We consider the set Ω2 of double zeros in (0, 1) for power series with coefficients in (−1, 0, 1). We prove that Ω2 is disconnected, and estimate minΩ2 with high accuracy. We also show that [2−1/2 − η, 1) ⊂ Ω2 for some small, but explicit, η > 0 (this was known only for η = 0). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine fractals.

Original languageEnglish
Pages (from-to)499-511
Number of pages13
JournalExperimental Mathematics
Volume15
Issue number4
DOIs
StatePublished - 2006
Externally publishedYes

Keywords

  • Self-affine fractals
  • Zeros of power series

Fingerprint

Dive into the research topics of 'Zeros of (−1, 0, 1) power series and connectedness loci for self-affine sets'. Together they form a unique fingerprint.

Cite this