Publikation: Valuation theory of exponential Hardy fields II : principal parts of germs in the Hardy field of o-minimal exponential expansions of the reals
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2017
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Kuhlmann, Franz-Viktor
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BROGLIA, Fabrizio, ed. and others. Ordered algebraic structures and related topics. Providence, Rhode Island: American Mathematical Society, 2017, pp. 227-238. Contemporary mathematics. 697. ISBN 978-1-4704-2966-9. Available under: doi: 10.1090/conm/697
Zusammenfassung
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 This paper is a follow up to \cite{[K-K2]} and is partially based on unpublished results of \cite{[K-K]}. A previous version \cite{[K-K1]} (which was dedicated to Murray A. Marshall on his 60th birthday) remained unpublished.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.
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510 Mathematik
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International Conference on Ordered Algebraic Structures and Related Topics, 12. Okt. 2015 - 16. Okt. 2015, Luminy, France
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KUHLMANN, Franz-Viktor, Salma KUHLMANN, 2017. Valuation theory of exponential Hardy fields II : principal parts of germs in the Hardy field of o-minimal exponential expansions of the reals. International Conference on Ordered Algebraic Structures and Related Topics. Luminy, France, 12. Okt. 2015 - 16. Okt. 2015. In: BROGLIA, Fabrizio, ed. and others. Ordered algebraic structures and related topics. Providence, Rhode Island: American Mathematical Society, 2017, pp. 227-238. Contemporary mathematics. 697. ISBN 978-1-4704-2966-9. Available under: doi: 10.1090/conm/697BibTex
@inproceedings{Kuhlmann2017Valua-36928.2,
year={2017},
doi={10.1090/conm/697},
title={Valuation theory of exponential Hardy fields II : principal parts of germs in the Hardy field of o-minimal exponential expansions of the reals},
number={697},
isbn={978-1-4704-2966-9},
publisher={American Mathematical Society},
address={Providence, Rhode Island},
series={Contemporary mathematics},
booktitle={Ordered algebraic structures and related topics},
pages={227--238},
editor={Broglia, Fabrizio},
author={Kuhlmann, Franz-Viktor and Kuhlmann, Salma}
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