A Diophantine definition of the constants in ℚ(z)

2022/08/24 by Garcia-Fritz, Natalia, Pasten, Hector
#11G05 #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT) #Primary: 11U09 #Secondary: 14J27

paper · doi:10.48550/arxiv.2208.11616

Abstract

It is an old problem in the area of Diophantine definability to determine whether ℚ is Diophantine in ℚ(z). We provide a positive answer conditional on two standard conjectures on elliptic surfaces.

Related

• Defining ℤ in ℚ
• \mathbb Q∖\mathbb Z is diophantine over \mathbb Q with 7 unknowns
• Elliptic divisibility sequences and undecidable problems about rational points
• Diophantine Quadruples and Cayley's Hyperdeterminant
• Diophantine properties for q-analogues of Dirichlet's beta function at positive integers