A characterization of sums of $2n$th powers of global meromorphic functions
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- by JesĂşs M. Ruiz PDF
- Proc. Amer. Math. Soc. 109 (1990), 915-923 Request permission
Abstract:
Let $M$ be a real analytic manifold. In this note we prove Theorem. Let $X$ be a compact analytic set of $M$ and $\sum$ its singular locus. Then, a meromorphic function $h$ on $X$ is a sum of $2n$-th powers of meromorphic functions if and only if, for every analytic curve $\sigma :\left ( { - \varepsilon ,\varepsilon } \right ) \to X$ not contained in $\sum$, it holds $h \circ \sigma = a{t^m} + \cdots$, with $a > 0$ and $2n$ dividing $m$.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 915-923
- MSC: Primary 32C25; Secondary 12D15
- DOI: https://doi.org/10.1090/S0002-9939-1990-1023347-0
- MathSciNet review: 1023347