Submission date: 18 June 2024

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 ρ ≥ 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.

Mathematics Subject Classification: Primary: 03B25, Secondary: 30D15, 11U05

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Full text arXiv 2406.12791: pdf, ps.