Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 58, Number 1 (2014), 279-284.
On the exceptional set in a conditional theorem of Littlewood
In 1952, Littlewood stated a conjecture about the average growth of spherical derivatives of polynomials, and showed that it would imply that for entire function of finite order, “most” preimages of almost all points are concentrated in a small subset of the plane. In 1988, Lewis and Wu proved Littlewood’s conjecture. Using techniques from complex dynamics, we construct entire functions of finite order with a bounded set of singular values for which the set of exceptional preimages is infinite, with logarithmically growing cardinality.
Illinois J. Math., Volume 58, Number 1 (2014), 279-284.
First available in Project Euclid: 1 April 2015
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Geyer, Lukas. On the exceptional set in a conditional theorem of Littlewood. Illinois J. Math. 58 (2014), no. 1, 279--284. doi:10.1215/ijm/1427897178. https://projecteuclid.org/euclid.ijm/1427897178