1. Ordered Algebraic Structures and Related Topics
- Author
-
Franz-Viktor Kuhlmann and Salma Kuhlmann
- Subjects
Power series ,Conjecture ,Diophantine equation ,010102 general mathematics ,Context (language use) ,0102 computer and information sciences ,01 natural sciences ,Exponential function ,Combinatorics ,010201 computation theory & mathematics ,Hardy field ,0101 mathematics ,Structured program theorem ,Mathematics ,Analytic function - Abstract
We present a general structure theorem for the Hardy field of an o-minimal expansion of the reals by restricted analytic functions and an unrestricted exponential. We proceed to analyze its residue fields with respect to arbitrary convex valuations, and deduce a power series expansion of exponential germs. We apply these results to cast "Hardy's conjecture" (see \cite[p.111]{[KS]}) in a more general framework. This paper is a follow up to \cite{[K-K2]} and is partially based on unpublished results of \cite{[K-K]}. A previous version \cite{[K-K1]} (which was dedicated to Murray A. Marshall on his 60th birthday) remained unpublished. In \cite{[W]} our structure theorem for the residue fields was rediscovered and applied to the diophantine context. Due to this revived interest, we decided to rework the preprint \cite{[K-K1]} and submit it to the Proceedings Volume.
- Published
- 2017