Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zeta functions and oscillatory integrals for meromorphic functions   In the 70's Igusa developed a uniform theory for local zeta functions and
oscillatory integrals attached to polynomials with coefficients in a local
field of characteristic zero. In the present article this theory is extended to
the case of rational functions, or, more generally, meromorphic functions f/g,
with coefficients in a local field of characteristic zero. This generalization
is far from being straightforward due to the fact that several new geometric
phenomena appear. Also, the oscillatory integrals have two different asymptotic
expansions: the 'usual' one when the norm of the parameter tends to infinity,
and another one when the norm of the parameter tends to zero. The first
asymptotic expansion is controlled by the poles (with negative real parts) of
all the twisted local zeta functions associated to the meromorphic functions
f/g - c, for certain special values c. The second expansion is controlled by
the poles (with positive real parts) of all the twisted local zeta functions
associated to f/g.

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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con