Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension Free Growth Results for Vector-Valued Functions of Several
  Complex Variables   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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The categories of this paper are: hep-th
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph