The Diophantine problem for rings of exponential polynomials

• Autores: Dimitra Chompitaki, Natalia Garcia-Fritz, Hector Pasten, Thanases Pheidas, Xavier Vidaux
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 23, Nº 4, 2022, págs. 1625-1636
• Idioma: inglés
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• Resumen

  • 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.