@article{Kaiser2019Analy-40967.2,
  year={2019},
  doi={10.1090/tran/7748},
  title={Analytic continuations of log-exp-analytic germs},
  number={7},
  volume={371},
  issn={0002-9947},
  journal={Transactions of the American Mathematical Society (TRAN)},
  pages={5203--5246},
  author={Kaiser, Tobias and Speissegger, Patrick}
}

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    <dcterms:abstract xml:lang="eng">We describe maximal, in a sense made precise, L-analytic continuations of germs at +∞ of unary functions definable in the o-minimal structure R&lt;sub&gt;an,exp&lt;/sub&gt; on the Riemann surface L of the logarithm. As one application, we give an upper bound on the logarithmic-exponential complexity of the compositional inverse of an infinitely increasing such germ, in terms of its own logarithmic-exponential complexity and its level. As a second application, we strengthen Wilkie’s theorem on definable complex analytic continuations of germs belonging to the residue field R&lt;sub&gt;poly&lt;/sub&gt; of the valuation ring of all polynomially bounded definable germs.</dcterms:abstract>
    <dc:contributor>Kaiser, Tobias</dc:contributor>
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