Hilbert's tenth problem for lacunary entire functions of finite order
Logic
2023-08-11 v1 Complex Variables
Abstract
In the context of Hilbert's tenth problem, an outstanding open case is that of complex entire functions in one variable. A negative solution is known for polynomials (by Denef) and for exponential polynomials of finite order (by Chompitaki, Garcia-Fritz, Pasten, Pheidas, and Vidaux), but no other case is known for rings of complex entire functions in one variable. We prove a negative solution to the analogue of Hilbert's tenth problem for rings of complex entire functions of finite order having lacunary power series expansion at the origin.
Keywords
Cite
@article{arxiv.2308.05714,
title = {Hilbert's tenth problem for lacunary entire functions of finite order},
author = {Natalia Garcia-Fritz and Hector Pasten},
journal= {arXiv preprint arXiv:2308.05714},
year = {2023}
}