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

• Autorzy: Oleg Petrushov
• Języki publikacji: EN

Abstrakty

EN

We consider the behavior of the power series $𝔐_0(z) = ∑_{n=1}^{∞} μ^2(n)z^n$ as z tends to $e(β) = e^{2πiβ}$ along a radius of the unit circle. If β is irrational with irrationality exponent 2 then $𝔐_0(e(β)r) = O((1-r)^{-1/2-ε})$. Also we consider the cases of higher irrationality exponent. We prove that for each δ there exist irrational numbers β such that $𝔐_0(e(β)r) = Ω((1-r)^{-1+δ})$.

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: 2015
• Tom: 168
• Numer: 1
• Strony: 17-30

Daty

wydano

2015

Twórcy

autor

Oleg Petrushov

• Moscow State University, Vorobyovy Gory, Moscow, Russia

Identyfikatory

DOI

10.4064/aa168-1-2