The order conjecture fails in S

Abstract

We construct an entire function $f$ with only three singular values whose order of growth can change under a quasiconformal equivalence. This is a counterexample to the Order Conjecture in the Speiser class $\mathcal{S}$ of entire functions.

arXiv comment23 pages, 18 figures

Cited by in corpus (4)

• On invariance of order and the area property for finite-type entire functions
• The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class
• The Hausdorff dimension of escaping sets of meromorphic functions in the Speiser class
• Hausdorff dimension of escaping sets of meromorphic functions