TY  - JOUR
A1  - Gräter, Joachim
A1  - Weese, Martin
T1  - On the norm equation over function fields
N2  - If K is an algebraic function field of one variable over an algebraically closed field k and F is a finite extension of K, then any element a of K can be written as a norm of some b in F by Tsen's theorem. All zeros and poles of a lead to zeros and poles of b, but in general additional zeros and poles occur. The paper shows how this number of additional zeros and poles of b can be restricted in terms of the genus of K, respectively F. If k is the field of all complex numbers, then we use Abel's theorem concerning the existence of meromorphic functions on a compact Riemarm surface. From this, the general case of characteristic 0 can be derived by means of principles from model theory, since the theory of algebraically closed fields is model-complete. Some of these results also carry over to the case of characteristic p > 0 using standard arguments from valuation theory
Y1  - 2004
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/15160
SN  - 0024-6107
ER  -