Hilbert's Tenth Problem for rational function fields over p-adic fields

Details Hilbert's Tenth Problem for rational function fields over p-adic fields Hilbert's Tenth Problem for rational function fields over p-adic fields

2011-06-24

arxiv.org/abs/1106.4912v1

Mathematics

Logic

Scientific paper

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 over K and apply it to prove isotropy for a certain class of quadratic forms over K(t). Using this result, we give an existential definition for the predicate "v_t(x) >= 0" in K(t). This implies undecidability of diophantine equations over K(t).

Affiliated with

Also associated with

No associations

Rating

Hilbert's Tenth Problem for rational function fields over p-adic fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hilbert's Tenth Problem for rational function fields over p-adic fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hilbert's Tenth Problem for rational function fields over p-adic fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-393813