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Preprint Number 467

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467. Alex Wilkie
Some results and problems on complex germs with definable Mittag-Leffler stars
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Submission date: 15 June 2012.

Abstract:

Working in an o-minimal expansion of the real field, we investigate when a germ (around 0 say) of a complex analytic function has a definable analytic continuation to its Mittag-Lffler star.
As an application we show that any algebro-logarithmic function that is complex analytic in a neighbourhood of the origin in C has an analytic continuation to all but finitely many points in C.

It is my pleasure to dedicate this paper to Anand Pillay on the occasion of his 60th birthday.

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