Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Integer group determinants for the Heisenberg group of order $p^3$   We establish a congruence satisfied by the integer group determinants for the
non-abelian Heisenberg group of order $p^3$. We characterize all determinant
values coprime to $p$, give sharp divisibility conditions for multiples of $p$,
and determine all values when $p=3$. We also provide new sharp conditions on
the power of $p$ dividing the group determinants for $\mathbb Z_p^2$.
  For a finite group, the integer group determinants can be understood as
corresponding to Lind's generalization of the Mahler measure. We speculate on
the Lind-Mahler measure for the discrete Heisenberg group and for two other
infinite non-abelian groups arising from symmetries of the plane and 3-space.

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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph