# Hilbert’s tenth problem for algebraic function fields of characteristic 2

```@article{Eisentraeger2002HilbertsTP,
title={Hilbert’s tenth problem for algebraic function fields of characteristic 2},
author={Kirsten Eisentraeger},
journal={Pacific Journal of Mathematics},
year={2002},
volume={210},
pages={261-281}
}```
Let K be an algebraic function field of characteristic 2 with constant field C K . Let C be the algebraic closure of a finite field in K. Assume that C has an extension of degree 2. Assume that there are elements u, x of K with u transcendental over C K and x algebraic over C(u) and such that K = C K (u,x). Then Hilbert's Tenth Problem over K is undecidable. Together with Shlapentokh's result for odd characteristic this implies that Hilbert's Tenth Problem for any such field K of finite… Expand
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