On the finiteness of Pythagoras numbers of real meromorphic functions
摘要
We consider the 17th Hilbert Problem for global analytic functions in a modified form that involves infinite sums of squares. Then we prove a local-global principle for an analytic function to be a sum of squares. We deduce that an affirmative solution to the 17th Hilbert Problem for global analytic functions implies the finiteness of the Pythagoras number of the fields: (i) of global meromorphic functions, and (ii) of meromorphic function germs. This measures the difficulty of the problem in the analytic case.
引用本文（GB/T 7714）
Francesca Acquistapace, Fabrizio Broglia, José F. Fernando, 等. On the finiteness of Pythagoras numbers of real meromorphic functions[J]. Bulletin de la Société mathématique de France, 2010.
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