This article is cited in 9 papers

The least type of an entire function of order $\rho\in(0,1)$ having positive zeros with prescribed averaged densities

G. G. Braichev

Moscow State Pedagogical University

Abstract: The problem of the least type of entire functions of order $\rho\in(0,1)$ all of whose zeros lie on the same ray and have the prescribed upper and lower averaged $\rho$-densities is solved. A complete investigation of the value of the extremal type is carried out, including a description of its asymptotic behaviour.
Bibliography: 14 titles.

Keywords: extremal type of an entire function, upper and lower averaged density of zeros.

UDC: 517.547.2

MSC: 30D15

Received: 21.04.2011 and 05.02.2012

DOI: 10.4213/sm7879

 English version: Sbornik: Mathematics, 2012, 203:7, 950–975

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