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PreprintarXiv licencearXiv

A counterexample to Fuchs's conjecture

  • Alexandre Eremenko
  • Teng Zhang
Open at sourcePDFDOICite

Abstract

For every ρ in (0, 1/2), we construct an entire function F of order ρ whose logarithmic derivative has zero as a deficient value. This disproves an old conjecture of W. H. J. Fuchs.

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Cite

BibTeXRIS
BibTeX
@misc{eremenko2026counterexample,
  title = {{A counterexample to Fuchs's conjecture}},
  author = {Alexandre Eremenko and Teng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28443},
  eprint = {2609.28443},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28443},
}
RIS
TY  - UNPB
TI  - A counterexample to Fuchs's conjecture
AU  - Alexandre Eremenko
AU  - Teng Zhang
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28443
UR  - https://arxiv.org/abs/2609.28443
AB  - For every ρ in (0, 1/2), we construct an entire function F of order ρ whose logarithmic derivative has zero as a deficient value. This disproves an old conjecture of W. H. J. Fuchs.
ER  -