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# 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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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

@techreport{Kuhlmann2017Valua-36928, title={Valuation theory of exponential Hardy fields II : Principal parts of germs in the Hardy field of o-minimal exponential expansions of the reals}, year={2017}, author={Kuhlmann, Franz-Viktor and Kuhlmann, Salma}, note={Wird erscheinen in: AMS Contemporary Mathematics} }

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/36928"> <dc:contributor>Kuhlmann, Franz-Viktor</dc:contributor> <dc:language>eng</dc:language> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/36928"/> <dcterms:title>Valuation theory of exponential Hardy fields II : Principal parts of germs in the Hardy field of o-minimal exponential expansions of the reals</dcterms:title> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-01-24T13:31:08Z</dcterms:available> <dcterms:issued>2017</dcterms:issued> <dc:creator>Kuhlmann, Franz-Viktor</dc:creator> <dc:contributor>Kuhlmann, Salma</dc:contributor> <dc:creator>Kuhlmann, Salma</dc:creator> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-01-24T13:31:08Z</dc:date> <dcterms:abstract xml:lang="eng">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 This paper is a follow up to \cite{[K-K2]} and is partially based on unpublished results of \cite{[K-K]}. A previous version \cite{[K-K1]} (which was dedicated to Murray A. Marshall on his 60th birthday) remained unpublished.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.</dcterms:abstract> </rdf:Description> </rdf:RDF>