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arXiv · 2210.10556

Non-Diophantine sets in rings of functions

Natalia Garcia-Fritz·Hector Pasten·Thanases Pheidas
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Abstract

Except for a limited number of cases, a complete classification of the Diophantine sets of polynomial rings and fields of rational functions seems out of reach at present. We contribute to this problem by proving that several natural sets and relations over these structures are not Diophantine.

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Natalia Garcia-Fritz, Hector Pasten, Thanases Pheidas. 2022-10-19. Non-Diophantine sets in rings of functions. https://arxiv.org/abs/2210.10556

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