Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bounds on the class number of algebraic function fields defined
  over any finite field   We give lower bounds on the number of effective divisors of degree $\leq g-1$
with respect to the number of places of certain degrees of an algebraic
function field of genus $g$ defined over a finite field. We deduce lower bounds
and asymptotics for the class number, depending mainly on the number of places
of a certain degree. We give examples of towers of algebraic function fields
having a large class number.

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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: physics