Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Slopes of modular forms and the ghost conjecture, II   In a previous article, we constructed an entire power series over $p$-adic
weight space (the 'ghost series') and conjectured, in the $\Gamma_0(N)$-regular
case, that this series encodes the slopes of overconvergent modular forms of
any $p$-adic weight. In this paper, we construct 'abstract ghost series' which
can be associated to various natural subspaces of overconvergent modular forms.
This abstraction allows us to generalize our conjecture to, for example, the
case of slopes of overconvergent modular forms with a fixed residual
representation that is locally reducible at $p$. Ample numerical evidence is
given for this new conjecture. Further, we prove that the slopes computed by
any abstract ghost series satisfy a distributional result at classical weights
(consistent with conjectures of Gouv\^ea) while the slopes form unions of
arithmetic progressions at all weights not in $\mathbf{Z}_p$.

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The categories of this paper are: econ
8
The categories of this paper are: hep-ex
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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: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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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: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con