Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The argument principle and holomorphic extendibility to finite Riemann
  surfaces   Let M be a finite Riemann surface and let A(bM) be the algebra of all
continuous functions on bM which extend holomorphically through M. We prove
that a continuous function F on bM belongs to A(bM) if for each f, g in A(bM)
such that fF+g has no zero the change of argument of fF+g along bM is
nonnegative.

27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat