Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple $q$-Zeta Values   We introduce a $q$-analog of the multiple harmonic series commonly referred
to as multiple zeta values. The multiple $q$-zeta values satisfy a $q$-stuffle
multiplication rule analogous to the stuffle multiplication rule arising from
the series representation of ordinary multiple zeta values. Additionally,
multiple $q$-zeta values can be viewed as special values of the multiple
$q$-polylogarithm, which admits a multiple Jackson $q$-integral representation
whose limiting case is the Drinfel'd simplex integral for the ordinary multiple
polylogarithm when $q=1$. The multiple Jackson $q$-integral representation for
multiple $q$-zeta values leads to a second multiplication rule satisfied by
them, referred to as a $q$-shuffle. Despite this, it appears that many
numerical relations satisfied by ordinary multiple zeta values have no
interesting $q$-extension. For example, a suitable $q$-analog of Broadhurst's
formula for $\zeta(\{3,1\}^n)$, if one exists, is likely to be rather
complicated. Nevertheless, we show that a number of infinite classes of
relations, including Hoffman's partition identities, Ohno's cyclic sum
identities, Granville's sum formula, Euler's convolution formula, Ohno's
generalized duality relation, and the derivation relations of Ihara and Kaneko
extend to multiple $q$-zeta values.

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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: stat