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Transactions of the American Mathematical Society
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Preprint . 2018
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https://dx.doi.org/10.48550/ar...
Article . 2018
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Logarithmic hyperseries

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jul 2019Embargo end date: 01 Jan 2018 France English Publisher:American Mathematical Society (AMS)Journal:Transactions of the American Mathematical Society, volume 372, pages 5,199-5,241 (issn: 0002-9947, eissn: 1088-6850, Copyright policy )
Authors: van den Dries, Lou; van der Hoeven, Joris; Kaplan, Elliot;

doi: 10.1090/tran/7876 , 10.48550/arxiv.1810.01810

arXiv: 1810.01810

Logarithmic hyperseries

Abstract

We define the field $\mathbb{L}$ of logarithmic hyperseries, construct on $\mathbb{L}$ natural operations of differentiation, integration, and composition, establish the basic properties of these operations, and characterize these operations uniquely by such properties.

42 pages

Country
France
Related Organizations
Keywords

Applications of model theory, Model-theoretic algebra, surreal numbers, Mathematics - Logic, Differential algebra, Hardy fields, logarithmic hyperseries, FOS: Mathematics, Logic (math.LO), Valuations, completions, formal power series and related constructions (associative rings and algebras), [INFO.INFO-MS]Computer Science [cs]/Mathematical Software [cs.MS], Model theory of ordered structures; o-minimality, transseries

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    popularity
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    influence
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green
bronze