050 Walter Van Assche

050 Walter Van Assche
Hermite-Padé approximation to two functions with branch points // Abstract: Hermite-Padé approximation to two functions is rational approximation to both functions with a common denominator and close contact at one point (we will use infinity). The common denominator is a polynomial with orthogonality conditions for two measures. If the two functions have branch points in the complex plane, then the asymptotic behaviour of the zeros (the poles of the Hermite-Padé approximants) is determined by algebraic functions satisfying a cubic relation. We will sketch how to get the full asymptotics of the common denominator using the Riemann-Hilbert problem for matrix valued functions for some particular choices of branch points, which appear in applications in number theory.
Rod Halburd
54
7/6/2021
00:57:47
CAvid, Complex Analysis