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

2024/06/18 by Hector Pasten, Héctor Pastén, Pasten, Hector
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #advanced mathematical theories #math.CV #math.LO #math.NT

paper · pdf · doi:10.48550/arxiv.2406.12791

openalex publication_date 2024/06/18 · openalex created_date 2024/06/20 · openalex updated_date 2026/07/28

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. In the direction of 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.

Related

• Hilbert's tenth problem for lacunary entire functions of finite order
• The Diophantine problem for rings of exponential polynomials
• Hilbert's tenth problem via additive combinatorics
• Hilbert's Tenth Problem for some Noncommutative Rings
• Hilbert's tenth problem for complex meromorphic functions in several variables