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

Oleg Petrushov. "On the behaviour close to the unit circle of the power series with Möbius function coefficients." Acta Arithmetica 164.2 (2014): 119-136. <http://eudml.org/doc/279145>.

@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 -