On the behaviour close to the unit circle of the power series with Möbius function coefficients
Oleg Petrushov
Acta Arithmetica, Tome 166 (2014), p. 119-136 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Let (z)=∑n=1∞μ(n)zn. We prove that for each root of unity e(β)=e2πiβ 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.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:279145 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-2,
     author = {Oleg Petrushov},
     title = {On the behaviour close to the unit circle of the power series with M\"obius function coefficients},
     journal = {Acta Arithmetica},
     volume = {166},
     year = {2014},
     pages = {119-136},
     zbl = {1304.11113},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-2}
}

Oleg Petrushov. On the behaviour close to the unit circle of the power series with Möbius function coefficients. Acta Arithmetica, Tome 166 (2014) pp. 119-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-2/