Analytic continuations of log-exp-analytic germs

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KAISER, Tobias, Patrick SPEISSEGGER, 2019. Analytic continuations of log-exp-analytic germs. In: Transactions of the American Mathematical Society (TRAN). 371(7), pp. 5203-5246. ISSN 0002-9947. eISSN 1088-6850. Available under: doi: 10.1090/tran/7748

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

eng Speissegger, Patrick Speissegger, Patrick Analytic continuations of <sup>log-exp</sup>-analytic germs Kaiser, Tobias terms-of-use 2019-04-09T12:59:48Z 2019-04-09T12:59:48Z Kaiser, Tobias 2019 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.

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