On the 'pits effect' of Littlewood and Offord

被引：8

作者：

Eremenko, Alexandre ^{[1
]}

Ostrovskii, Iossif ^{[2
]}

机构：

[1] Purdue Univ, W Lafayette, IN 47907 USA

[2] Bilkent Univ, TR-06533 Ankara, Turkey

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2007年 / 39卷

基金：

美国国家科学基金会;

关键词：

D O I：

10.1112/blms/bdm079

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Asymptotic behaviour of the entire functions f(z) = Sigma(infinity)(n=0) e(2 pi in alpha n) z(n)/n!, with real an is studied. It turns out that the Phragmennn-Lindelof indicator of such a function is always non-negative, unless f( z) = e(az). For a special choice of alpha(n) = alpha n(2) with irrational alpha, the indicator is constant and f has completely regular growth in the sense of Levin and Pfluger. Similar functions of arbitrary order are also considered.

引用

页码：929 / 939

页数：11

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