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Dimension Free Growth Results for Vector-Valued Functions of Several Complex Variables

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arxiv 2201.12321 v1 pith:6AKDJE6G submitted 2022-01-28 math.CV

Faruk F. Abi-Khuzam This is my paper · ORCID
classification math.CV
keywords bestfunctionpossiblecomplexcorrespondingd-dimensionaldimensionentire
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Let f be an entire function of finite order less than 1. The maximum modulus M(r) of f and the counting function of the zeros N(r) are connected by a best possible growth inequality known as Valiron's Theorem: For functions subharmonic in d-dimensional Euclidean space, Hayman obtained a corresponding result with a best possible constant involving the dimension d. For the special case of an entire function on d-dimensional complex space, we obtain a corresponding dimension-free, best possible inequality.

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