On the behavior close to the unit circle of the power series whose coefficients are squared Möbius function values

Oleg Petrushov

Oleg Petrushov

Acta Arithmetica, Tome 168 (2015), p. 17-30 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider the behavior of the power series $_{0} (z) = \sum_{n = 1}^{\infty} μ^{2} (n) z^{n}$ as z tends to $e (β) = e^{2 π i β}$ along a radius of the unit circle. If β is irrational with irrationality exponent 2 then $_{0} (e (β) r) = O ({(1 - r)}^{- 1 / 2 - ε})$ . Also we consider the cases of higher irrationality exponent. We prove that for each δ there exist irrational numbers β such that $_{0} (e (β) r) = Ω ({(1 - r)}^{- 1 + δ})$ .

Publié le : 2015-01-01

Zbl 1331.11086

EUDML-ID : urn:eudml:doc:279033

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     author = {Oleg Petrushov},
     title = {On the behavior close to the unit circle of the power series whose coefficients are squared M\"obius function values},
     journal = {Acta Arithmetica},
     volume = {168},
     year = {2015},
     pages = {17-30},
     zbl = {1331.11086},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa168-1-2}
}

Oleg Petrushov. On the behavior close to the unit circle of the power series whose coefficients are squared Möbius function values. Acta Arithmetica, Tome 168 (2015) pp. 17-30. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa168-1-2/