3 papers
math.LO2011
Hilbert's Tenth Problem for rational function fields over p-adic fields
Claudia Degroote, Jeroen Demeyer
Let K be a p-adic field (a finite extension of some Q_p) and let K(t) be the field of rational functions over K. We define a kind of quadratic reciprocity symbol for polynomials ov…
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].