English

The order conjecture fails in S

Complex Variables 2020-07-13 v1

Abstract

We construct an entire function ff 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 S{\mathcal S} of entire functions.

Cite

@article{arxiv.2007.05387,
  title  = {The order conjecture fails in S},
  author = {Christopher J. Bishop},
  journal= {arXiv preprint arXiv:2007.05387},
  year   = {2020}
}

Comments

23 pages, 18 figures

R2 v1 2026-06-23T17:01:15.439Z