Quasiminimality of complex powers

The complex field, equipped with the multivalued functions of raising to each complex power, is quasiminimal, proving a conjecture of Zilber and providing evidence towards his stronger conjecture that the complex exponential field is quasiminimal.Comment: 35 page

Some results and problems on complex germs with definable Mittag-Leffler stars

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-Leffler 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

Annual Report of the Board of Regents of the Smithsonian Institution, showing the operations, expenditures, and condition of the Institution for the year 1884

Annual Report of the Smithsonian Institution and National Museum. [2266] Research related to the American Indians