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math.NT2022
On the fibres of an elliptic surface where the rank does not jump
Jerson Caro, Hector Pasten
For a non-constant elliptic surface over defined over , it is a result of Silverman that the Mordell--Weil rank of the fibres is at least the rank of the…
math.NT2022
Non-Diophantine sets in rings of functions
Natalia Garcia-Fritz, Hector Pasten, Thanases Pheidas
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 contr…
math.NT2022
A Diophantine definition of the constants in
Natalia Garcia-Fritz, Hector Pasten
It is an old problem in the area of Diophantine definability to determine whether is Diophantine in . We provide a positive answer conditional on two st…