Asymptotic estimates for the canonical products with zeros of a particular form

A. A. Yukhimenko

Lomonosov State University, Moscow, Russia

Abstract: We obtain sharp asymptotic estimates on the whole complex plane for the canonical products with zeros of the form $\lambda_n=-n^\alpha l(n)$, where $\alpha>0$ and $l(t)$ is a slowly varying function.

Keywords: canonical product, asymptotic estimate, slowly varying function.

UDC: 517.547.2

Received: 14.05.2009

 English version: Siberian Mathematical Journal, 2010, 51:4, 755–764

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