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arXiv · 2201.12321

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

Faruk F. Abi-Khuzam
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Abstract

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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Faruk F. Abi-Khuzam. 2022-01-28. Dimension Free Growth Results for Vector-Valued Functions of Several Complex Variables. https://arxiv.org/abs/2201.12321

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