Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds on the period of the continued fraction after a M\"obius
  transformation   We study M\"obius transformations (also known as linear fractional
transformations) of quadratic numbers. We construct explicit upper and lower
bounds on the period of the continued fraction expansion of a transformed
number as a function of the period of the continued fraction expansion of the
original number. We provide examples that show that the bound is sharp.

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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg