RT Journal Article
T1 On the finiteness of Pythagoras numbers of real meromorphic functions.
A1 Acquistapace, Francesca
A1 Broglia, Fabrizio
A1 Fernando Galván, José Francisco
A1 Ruiz Sancho, Jesús María
AB We consider the 17(th) Hilbert Problem for global real analytic functions in a modified form that involves infinite sums of squares. Then we prove a local-global principle for a real global analytic function to be a sum of squares of global real meromorphic functions. We deduce that an affirmative solution to the 17(th) Hilbert Problem for global real analytic functions implies the finiteness of the Pythagoras number of the field of global real meromorphic functions, hence that of the field of real meromorphic power series. This measures the difficulty of the 17(th) Hilbert problem in the analytic case.
PB French Mathematical Society
SN 0037-9484
YR 2010
FD 2010
LK https://hdl.handle.net/20.500.14352/42160
UL https://hdl.handle.net/20.500.14352/42160
NO Italian GNSAGA
NO INdAM
NO MIUR
NO Spanish GEOR
DS Docta Complutense
RD 8 may 2024