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Seminar on Complex Analysis (Gonchar Seminar)
January 29, 2018 17:00–19:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)

On Hermite–Padé approximants for the product of logarithms

V. G. Lysov

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow

Abstract: The talk is devoted to the Hermite–Padé approximants for the systems of functions containing $\ln(1+1/z)\ln(1-1/z)$. We consider two constructions for which an explicit form of approximations can be found. We study their asymptotics and convergence. We discuss number-theoretic applications related to Diophantine approximations of products of logarithms.