PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On the behavior close to the unit circle of power series with additive coefficients

Volume 180 / 2017

Oleg A. Petrushov Acta Arithmetica 180 (2017), 319-332 MSC: Primary 11N37; Secondary 30B30. DOI: 10.4064/aa8536-4-2017 Published online: 1 September 2017


Consider the power series $\mathfrak{A}(z)= \sum_{n=1}^{\infty}\alpha(n)z^n$, where $\alpha(n)$ is an additive function satisfying the condition $\alpha(p^m)=mf(p,m)\ln p$, where $f(p,m)\to 0$ as $p\to \infty$ uniformly with respect to $m$. Denote by $e(l/q)$ the root of unity $e^{2\pi il/q}$. For such series we give effective omega-estimates for $\mathfrak{A}(e(l/p^k)r)$ as $r\to 1-$. From the estimates we deduce that if such a series has non-singular points on the unit circle then it is a rational function.


  • Oleg A. PetrushovMoscow State University
    Vorobyovi Gory, Russia

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image