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Bulletin of the London Mathematical Society Advance Access originally published online on November 18, 2007
Bulletin of the London Mathematical Society 2007 39(6):929-939; doi:10.1112/blms/bdm079
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© 2007 London Mathematical Society

On the ‘pits effect’ of Littlewood and Offord

Alexandre Eremenko

Purdue University
West Lafayette, IN 47907-2067
USA

Iossif Ostrovskii

Bilkent University
Bilkent
Ankara 06533
Turkey

Received 19 September 2006. Revision received 27 April 2007.

Asymptotic behaviour of the entire functions Formula, with real {alpha}n is studied. It turns out that the Phragmén–Lindelöf indicator of such a function is always non-negative, unless f(z)=eaz. For a special choice of {alpha}n={alpha} n2 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.

2000 Mathematics Subject Classification 30D10, 30D15, 30B10.

First author supported by the NSF grants DMS-0555279 and DMS-0244547.


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