Some results and problems on complex germs with definable mittag-leffler stars

A. J. Wilkie

doi:10.1215/00294527-2143979

Some results and problems on complex germs with definable mittag-leffler stars

A. J. Wilkie

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Abstract

Working in an o-minimal expansion of the real field, we investigate when a germ (around zero, say) of a complex analytic function has a definable analytic continuation to its Mittag-Leffler star. As an application we show that any algebro-logarithmic function that is complex analytic in a neighborhood of the origin in C has an analytic continuation to all but finitely many points in C. © 2013 by University of Notre Dame. © 2013 by University of Notre Dame.

Original language	English
Pages (from-to)	603-610
Number of pages	7
Journal	Notre Dame Journal of Formal Logic
Volume	54
Issue number	3-4
DOIs	https://doi.org/10.1215/00294527-2143979
Publication status	Published - 2013

Keywords

Analytic continuation
Definable functions
O-minimality

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AB - Working in an o-minimal expansion of the real field, we investigate when a germ (around zero, say) of a complex analytic function has a definable analytic continuation to its Mittag-Leffler star. As an application we show that any algebro-logarithmic function that is complex analytic in a neighborhood of the origin in C has an analytic continuation to all but finitely many points in C. © 2013 by University of Notre Dame. © 2013 by University of Notre Dame.

KW - Analytic continuation

KW - Definable functions

KW - O-minimality

U2 - 10.1215/00294527-2143979

DO - 10.1215/00294527-2143979

M3 - Article

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VL - 54

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EP - 610

JO - Notre Dame Journal of Formal Logic

JF - Notre Dame Journal of Formal Logic

IS - 3-4

ER -

Some results and problems on complex germs with definable mittag-leffler stars

Abstract

Keywords

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