2023/08/10 by Garcia-Fritz, Natalia, Pasten, Hector
#30B10 #Complex Variables (math.CV) #FOS: Mathematics #Logic (math.LO) #Primary: 03B25 #Secondary: 11U05
paper · doi:10.48550/arxiv.2308.05714
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.