Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Several new product identities in relation to two-variable
  Rogers-Ramanujan type sums and mock theta functions   Product identities in two variables $x, q$ expand infinite products as
infinite sums, which are linear combinations of theta functions; famous
examples include Jacobi's triple product identity, Watson's quintuple identity,
and Hirschhorn's septuple identity. We view these series expansions as
representations in canonical bases of certain vector spaces of quasiperiodic
meromorphic functions (related to sections of line and vector bundles), and
find new identities for two nonuple products, an undecuple product, and several
two-variable Rogers-Ramanujan type sums. Our main theorem explains a
correspondence between the septuple product identity and the two original
Rogers-Ramanujan identities, involving two-variable analogues of fifth-order
mock theta functions. We also prove a similar correspondence between an octuple
product identity of Ewell and two simpler variations of the Rogers-Ramanujan
identities, which is related to third-order mock theta functions, and
conjecture other occurrences of this phenomenon. As applications, we specialize
our results to obtain identities for quotients of generalized Dedekind eta
functions and mock theta functions.

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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: stat
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin