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math.NT2009
Hilbert's Tenth Problem for function fields over valued fields in characteristic zero
Jeroen Demeyer
Let K be a field with a valuation satisfying the following conditions: both K and the residue field k have characteristic zero; the value group is not 2-divisible; there exists a m…
math.NT2008
Diophantine sets of polynomials over number fields
Jeroen Demeyer
Let R be a recursive subring of a number field. We show that recursively enumerable sets are diophantine for the polynomial ring R[Z].