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The distribution of the values of a random power series in the unit disk

Published online by Cambridge University Press:  14 November 2011

Matthias Jakob  and
A. C. Offord
Matthias Jakob
Affiliation:
Potsdamerstr. 168, 1000 Berlin 30, B.R.D
A. C. Offord
Affiliation:
Imperial College of Science and Technology, London S.W.7
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Synopsis

This is a study of the family of power series where Σ αnZn has unit radius of convergence and the εn are independent random variables taking the values ±1 with equal probability. It is shown that if

then almost all these power series take every complex value infinitely often in the unit disk.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 3-4 , 1983 , pp. 251 - 263
Copyright
Copyright © Royal Society of Edinburgh 1983

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