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International Conference on Complex Analysis Dedicated to the Memory of Andrei Gonchar and Anatoliy Vitushkin
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Enumerative problem for Pell–Abel equation A. B. Bogatyrev Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow |
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Abstract: The Pell–Abel (PA) functional equation is the reincarnation of the famous Diophantine equation in the world of polynomials, considered N. H. Abel in 1826. The equation arises in many problems: reduction of Abelian integrals, elliptic billiards, the spectral problem for infinite Jacobi matrices, approximation theory, etc. If the PA equation has a nontrivial solution, then there are infinitely many of them, and all of them are expressed via a primitive solution having a minimum degree. Using graphical techniques, we find the number of connected components in the space of PA equations with the coefficient of a given degree and having a primitive solution of another given degree. Joint work with Quentin Gendron (UNAM Institute of Mathematics) https://arxiv.org/abs/2306.00884. Website: https://zoom.us/j/98008001815?pwd=OG1rTVRFRzFpY3RhZmE4MXFwckxMUT09 * ID: 980 0800 1815; Password: 055016 |
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