This article is cited in 3 papers

The least type of an entire function whose zeros have prescribed averaged densities and lie on rays or in a sector

G. G. Braichev

Moscow State Pedagogical University

Abstract: We consider the problem of the least possible type of entire functions whose zeros have fixed upper and lower averaged densities and lie in a given set. In particular, we solve this problem in several important cases: 1) all zeros lie in a sector, 2) all zeros lie between two straight lines; 3) all zeros lie on rays subdividing the complex plane into equal sectors.
Bibliography: 15 titles.

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

UDC: 517.547.22

MSC: Primary 30D15; Secondary 30D10

Received: 01.02.2015 and 07.08.2015

DOI: 10.4213/sm8483

 English version: Sbornik: Mathematics, 2016, 207:2, 191–225

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