English

Hilbert's tenth problem for rings of holomorphic functions of bounded order

Complex Variables 2024-06-19 v1 Logic Number Theory

Abstract

One of the main open problems in the context of extensions of Hilbert's tenth problem (HTP) is the case of the ring of complex entire functions in one variable. Our main result provides a step towards an answer: For every ρ0\rho\ge 0, we give a negative solution to the analogue of HTP in the ring of complex entire functions in one variable of growth order at most ρ\rho.

Keywords

Cite

@article{arxiv.2406.12791,
  title  = {Hilbert's tenth problem for rings of holomorphic functions of bounded order},
  author = {Hector Pasten},
  journal= {arXiv preprint arXiv:2406.12791},
  year   = {2024}
}