TY - JOUR
T1 - Zeros of (−1, 0, 1) power series and connectedness loci for self-affine sets
AU - Shmerkin, Pablo
AU - Solomyak, Boris
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
KW - Self-affine fractals
KW - Zeros of power series
UR - https://www.scopus.com/pages/publications/33947132118
U2 - 10.1080/10586458.2006.10128977
DO - 10.1080/10586458.2006.10128977
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SN - 1058-6458
VL - 15
SP - 499
EP - 511
JO - Experimental Mathematics
JF - Experimental Mathematics
IS - 4
ER -