A new counting function for the zeros of holomorphic curves

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Datum
2009-03-18MFO Scientific Program
Research in Pairs 2009Serie
Oberwolfach Preprints;2009,25Autor
Anderson, J. M.
Hinkkanen, Aimo
Metadata
Zur LanganzeigeOWP-2009-25
Zusammenfassung
Let $f_1,..., f_p$ be entire functions that do not all vanish at any point, so that $(f_1,..., f_p)$ is a holomorphic curve in $\mathbb{CP}^{p-1}$. We introduce a new and more careful notion of counting the order of the zero of a linear combination of the functions $f_1,..., f_p$ at any point where such a linear combination vanishes, and, if all the $f_1,..., f_p$ are polynomials, also at infinity. This enables us to formulate an inequality, which sometimes holds as an identity, that sharpens the classical results of Cartan and others.