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

• Autorzy: Oleg Petrushov
• Języki publikacji: EN

Abstrakty

EN

Let $𝔐 (z) = ∑_{n=1}^{∞} μ(n)z^n$. We prove that for each root of unity $e(β) = e^{2πiβ}$ there is an a > 0 such that $𝔐 (e(β)r) = Ω((1-r)^{-a})$ 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 𝔐 (z) we obtain omega-estimates for some finite sums.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 30B30: Boundary behavior of power series, over-convergence

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 164
• Numer: 2
• Strony: 119-136

Daty

wydano

2014

Twórcy

autor

Oleg Petrushov

• Faculty of Mechanics and Mathematics, Moscow State University, Vorobyovi Gory, Moscow, Russia

Identyfikatory

DOI

10.4064/aa164-2-2