RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
Video Library
Archive
Most viewed videos

Search
RSS
New in collection





You may need the following programs to see the files






Conference to the Memory of Anatoly Alekseevitch Karatsuba on Number theory and Applications
January 29, 2016 17:30, Dorodnitsyn Computing Centre, Department of Mechanics and Mathematics of Lomonosov Moscow State University., 119991, Moscow, Gubkina str., 8, Steklov Mathematical Institute, 9 floor, Conference hall
 


On a functional analog of the Thue-Siegel-Roth theorem

A. I. Aptekarev

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
Video records:
Flash Video 201.2 Mb
Flash Video 1,198.7 Mb
MP4 201.2 Mb

Number of views:
This page:202
Video files:86

A. I. Aptekarev


Видео не загружается в Ваш браузер:
  1. Установите Adobe Flash Player    

  2. Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080
  3. Сообщите администратору портала о данной ошибке

Abstract: Let $f$ be a germ (the power series expansion) of an algebraic function at infinity. We discuss the limiting properties of the convergents of a functional continued fraction with polynomial coefficients for $f$ (alternative names are diagonal Pade approximants or best local rational approximants). If we compare this functional continued fraction for $f$ with the usual continued fraction (with integer coefficients) for a real number, then the degree of the polynomial coefficient is analogous to the value (magnitude) of the integer coefficient. In our joint work with M. Yattselev [1], we derived strong (or Bernshtein-Szegö type) asymptotics for the denominators of the convergents of a functional continued fraction for analytic function with a finite number of branch points (which are in a generic position in the complex plane). One of the applications following from this result is a sharp estimate for a functional analog of the Thue-Siegel-Roth theorem.

Language: Russian and English

References
  1. A.I. Aptekarev, M.L. Yattselev, “Padé approximants for functions with branch points — strong asymptotics of Nuttall-Stahl polynomials”, Acta Math., 215:2 (2015), 217–280, arXiv: 1109.0332v2 [math.CA]  crossref  mathscinet  isi


SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2017