2020/04/01 by Dimitra Chompitaki, Natalia Garcia‐Fritz, Chompitaki, D. +7
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2004.00612
One of the main open problems regarding decidability of the existential theory of rings is the analogue of Hilbert's Tenth Problem (HTP) for the ring of entire holomorphic functions in one variable. In the direction of a negative solution, we prove unsolvability of HTP for rings of exponential polynomials. This provides the first known case of HTP for a ring of entire holomorphic functions in one variable strictly containing the polynomials. The technique of proof consists of an interaction between Arithmetic, Analysis, Logic, and Functional Transcendence.