On the behaviour close to the unit circle of the power series with Möbius function coefficients

@article{OlegPetrushov2014,
abstract = {Let $ (z) = ∑_\{n=1\}^\{∞\} μ(n)z^n$. We prove that for each root of unity $e(β) = e^\{2πiβ\}$ there is an a > 0 such that $ (e(β)r) = Ω((1-r)^\{-a\})$ as r → 1-. For roots of unity e(l/q) with q ≤ 100 we prove that these omega-estimates are true with a = 1/2. From omega-estimates for (z) we obtain omega-estimates for some finite sums.},
author = {Oleg Petrushov},
journal = {Acta Arithmetica},
keywords = {Möbius function; power series; omega estimates},
language = {eng},
number = {2},
pages = {119-136},
title = {On the behaviour close to the unit circle of the power series with Möbius function coefficients},
url = {http://eudml.org/doc/279145},
volume = {164},
year = {2014},
}

TY - JOUR
AU - Oleg Petrushov
TI - On the behaviour close to the unit circle of the power series with Möbius function coefficients
JO - Acta Arithmetica
PY - 2014
VL - 164
IS - 2
SP - 119
EP - 136
AB - Let $ (z) = ∑_{n=1}^{∞} μ(n)z^n$. We prove that for each root of unity $e(β) = e^{2πiβ}$ there is an a > 0 such that $ (e(β)r) = Ω((1-r)^{-a})$ as r → 1-. For roots of unity e(l/q) with q ≤ 100 we prove that these omega-estimates are true with a = 1/2. From omega-estimates for (z) we obtain omega-estimates for some finite sums.
LA - eng
KW - Möbius function; power series; omega estimates
UR - http://eudml.org/doc/279145
ER -