Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Igusa functions and ideal growth in nilpotent Lie rings   We introduce a new class of combinatorially defined rational functions and
apply them to deduce explicit formulae for local ideal zeta functions
associated to the members of a large class of nilpotent Lie rings which
contains the free class-2-nilpotent Lie rings and is stable under direct
products. Our results unify and generalize a substantial number of previous
computations. We show that the new rational functions, and thus also the local
zeta functions under consideration, enjoy a self-reciprocity property,
expressed in terms of a functional equation upon inversion of variables. We
establish a conjecture of Grunewald, Segal, and Smith on the uniformity of
normal zeta functions of finitely generated free class-2-nilpotent groups.

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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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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: astro-ph