Publikation: Analytic continuations of log-exp-analytic germs
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2019
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Transactions of the American Mathematical Society (TRAN). 2019, 371(7), pp. 5203-5246. ISSN 0002-9947. eISSN 1088-6850. Available under: doi: 10.1090/tran/7748
Zusammenfassung
We describe maximal, in a sense made precise, L-analytic continuations of germs at +∞ of unary functions definable in the o-minimal structure Ran,exp 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 Rpoly of the valuation ring of all polynomially bounded definable germs.
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510 Mathematik
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KAISER, Tobias, Patrick SPEISSEGGER, 2019. Analytic continuations of log-exp-analytic germs. In: Transactions of the American Mathematical Society (TRAN). 2019, 371(7), pp. 5203-5246. ISSN 0002-9947. eISSN 1088-6850. Available under: doi: 10.1090/tran/7748BibTex
@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<sub>an,exp</sub> 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<sub>poly</sub> of the valuation ring of all polynomially bounded definable germs.</dcterms:abstract>
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