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SUMMARY:Enumerative problem for Pell-Abel Equation
DTSTART:20260513T080000Z
DTEND:20260513T090000Z
DTSTAMP:20260505T134700Z
UID:indico-event-155@bscihub.com
DESCRIPTION:Speakers: Andrei Bogatyrev ((INM RAS\, MSU\, HSE\, MCFAM))\n\n
 The Pell–Abel (PA) functional equation P^2-DQ^2=1 is a reincarnation of 
 the famous Diophantine equation in the world of polynomials\, considered b
 y N.H. Abel in 1826. The equation arises in many problems: the reduction o
 f Abelian integrals\, elliptic billiards\, the spectral problem for infini
 te Jacobi matrices\, approximation theory\, and so on. If an PA equation 
 has a nontrivial solution (P\,Q)\\neq (1\,0)\, then there are infinitely m
 any of them\, and all of them are expressible in terms of a primitive solu
 tion of minimal degree. Using a graphical technique\, we find the number 
 of connected components in the space of PA equations with a coefficient D(
 x)  of a given degree and having a primitive solution P(x) of another giv
 en degree. \n \nJoint work with Quentin Gendron (Institute of Mathematic
 s\, UNAM)  \n“The space of solvable Pell-Abel equations”\, Compositi
 o Mathematica\, 161:7 (2025)\n\nhttps://bscihub.com/event/155/
URL:https://bscihub.com/event/155/
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