Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automorphic forms for some even unimodular lattices   We look at genera of even unimodular lattices of rank $12$ over the ring of
integers of $\mathbb{Q}(\sqrt{5})$ and of rank $8$ over the ring of integers of
$\mathbb{Q}(\sqrt{3})$, using Kneser neighbours to diagonalise spaces of
scalar-valued algebraic modular forms. We conjecture most of the global Arthur
parameters, and prove several of them using theta series, in the manner of
Ikeda and Yamana. We find instances of congruences for non-parallel weight
Hilbert modular forms. Turning to the genus of Hermitian lattices of rank $12$
over the Eisenstein integers, even and unimodular over $\mathbb{Z}$, we prove a
conjecture of Hentschel, Krieg and Nebe, identifying a certain linear
combination of theta series as an Hermitian Ikeda lift, and we prove that
another is an Hermitian Miyawaki lift.

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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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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: comp-gas