Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automatic sequences as good weights for ergodic theorems   We study correlation estimates of automatic sequences (that is, sequences
computable by finite automata) with polynomial phases. As a consequence, we
provide a new class of good weights for classical and polynomial ergodic
theorems, not coming themselves from dynamical systems.
  We show that automatic sequences are good weights in $L^2$ for polynomial
averages and totally ergodic systems. For totally balanced automatic sequences
(i.e., sequences converging to zero in mean along arithmetic progressions) the
pointwise weighted ergodic theorem in $L^1$ holds. Moreover, invertible
automatic sequences are good weights for the pointwise polynomial ergodic
theorem in $L^r$, $r>1$.

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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: eess