Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cyclicity and Maximal Multiplicity for Zeros of Families of Analytic
  Functions   Let f_{\lambda} be a family of holomorphic functions in the unit disk,
holomorphic in parameter \lambda\in U\subset\C^{n}. We estimate the number of
zeros of f_{\lambda} in a smaller disk via some characteristic of the ideal
generated by Taylor coefficients of f_{\lambda}. Our estimate is locally sharp
and improve the previous estimate obtained by Roytwarf and Yomdin.

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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph