seminar: Arithmetic Gevrey series. An arithmetic look at asymptotic analysis and special functions
speaker: Yves André (Institut de Mathématiques de Jussieu)abstract: A quite remarkable feature of the asymptotic analysis of analytic dynamical systems is the ubiquity of Gevrey series (formal power series whose n-th coefficient typically grows like some rational power of n! ), and the natural summability of such series in suitable sectors. Another remarkable but less-noticed feature of classical Gevrey series encountered in treatises on special functions is the arithmetic counterpart of this growth, namely the inversely proportional growth of the denominators of their (rational or algebraic) coefficients. It turns out that such arithmetic Gevrey series have strong rigidity properties, which account for the simple shape of the differential equations which they satisfy, and further, for the optimal transcendence properties of their special values at algebraic points.
timetable:
Tue 29 Jan, 14:00 - 15:00, Sala Conferenze Centro De Giorgi
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