On the Behavior of Power Series with Completely Additive Coefficients

• Autorzy: Oleg Petrushov
• Języki publikacji: EN

Abstrakty

EN

Consider the power series $𝔄(z) = ∑_{n=1}^{∞} α(n)zⁿ$, where α(n) is a completely additive function satisfying the condition α(p) = o(lnp) for prime numbers p. Denote by e(l/q) the root of unity $e^{2πil/q}$. We give effective omega-estimates for $𝔄(e(l/p^k)r)$ when r → 1-. From them we deduce that if such a series has non-singular points on the unit circle, then it is a zero function.

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: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2015
• Tom: 63
• Numer: 3
• Strony: 217-225

Daty

wydano

2015

Twórcy

autor

Oleg Petrushov

• Moscow State University, Moscow, Russia

Identyfikatory

DOI

10.4064/ba8018-1-2016