Submission date: 15 August 2017

Abstract:

We describe maximal, in a sense made precise, analytic continuations of germs at infinity of unary functions definable in the o-minimal structure R_an,exp on the Riemann surface 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 of the valuation ring of all polynomially bounded definable germs.

Mathematics Subject Classification: 03C99, 30H99

Keywords and phrases: O-minimal structures, log-exp-analytic germs, analytic continuation.

Full text arXiv 1708.04496: pdf, ps.