Hermite-Padé approximation to two function 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.

complex variables

Audience: researchers in the topic

CAvid: Complex Analysis video seminar

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