论文标题
指数多项式环的双磷酸问题
The Diophantine problem for rings of exponential polynomials
论文作者
论文摘要
关于环的存在理论的确定性的主要开放问题之一是希尔伯特第十问题（HTP）的类似物对于一个变量中整个霍明型函数的环。在负溶液的方向上，我们证明HTP对于指数多项式的环不明确。这提供了严格包含多项式的一个变量中整个全态函数环的HTP的第一个已知情况。证明技术包括算术，分析，逻辑和功能性超越之间的相互作用。
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.
