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Elliptic divisibility sequences and undecidable problems about rational points
Gunther Cornelissen, Karim Zahidi
Julia Robinson has given a first-order definition of the rational integers Z in the rational numbers Q by a formula (\forall \exists \forall \exists)(F=0) where the \forall-quantif…
Division-ample sets and the Diophantine problem for rings of integers
Gunther Cornelissen, Thanases Pheidas, Karim Zahidi
We prove that Hilbert's Tenth Problem for a ring of integers in a number field K has a negative answer if K satisfies two arithmetical conditions (existence of a so-called division…
Torsion of Drinfeld modules and equicharacteristic unimodular Galois covers
Gunther Cornelissen, Marina Tripolitaki
We prove that the groups PSL(r,q^d) can be realized F_q(T)-regularly as Galois groups over the purely transcendental field F_q(T)(t_1,...,t_{r-1}) if r is even and r/2 is coprime t…
The 2-primary class group of certain hyperelliptic curves
Gunther Cornelissen
Let G be the separable Galois group of a finite field F of characteristic p, and X/F an imaginary hyperelliptic curve such that G acts transitively on its set W(X) of Weierstrass p…