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Journal Article
ANALYTIC CONTINUATIONS OF log-exp-ANALYTIC GERMS
2019
Overview
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.
Publisher
American Mathematical Society
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