Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the spectrum of the Thue-Morse quasicrystal and the rarefaction
  phenomenon   The spectrum of a weighted Dirac comb on the Thue-Morse quasicrystal is
investigated, and characterized up to a measure zero set, by means of the
Bombieri-Taylor conjecture, for Bragg peaks, and of another conjecture that we
call Aubry-Godr\`eche-Luck conjecture, for the singular continuous component.
The decomposition of the Fourier transform of the weighted Dirac comb is
obtained in terms of tempered distributions. We show that the asymptotic
arithmetics of the $p$-rarefied sums of the Thue-Morse sequence (Dumont;
Goldstein, Kelly and Speer; Grabner; Drmota and Skalba,...), namely the
fractality of sum-of-digits functions, play a fundamental role in the
description of the singular continous part of the spectrum, combined with some
classical results on Riesz products of Peyri\`ere and M. Queff\'elec. The
dominant scaling of the sequences of approximant measures on a part of the
singular component is controlled by certain inequalities in which are involved
the class number and the regulator of real quadratic fields.

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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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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: solv-int
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys