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SUMMARY:Andrzej Dabrowski (University of Szczecin)
DTSTART:20211207T113000Z
DTEND:20211207T133000Z
DTSTAMP:20260422T102621Z
UID:FGC-IPM/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGC-IPM/6/">
 On a class of generalized Fermat equations of signature $(2\,2n\,3)$</a>\n
 by Andrzej Dabrowski (University of Szczecin) as part of FGC-HRI-IPM Numbe
 r Theory Webinars\n\n\nAbstract\nWe will discuss the generalized Fermat eq
 uations\n$Ax^2 + By^{2n} = 4z^3$\,  assuming (for simplicity) that\nthe cl
 ass number of the imaginary quadratic field\n$\\mathbb Q(\\sqrt{-AB})$ is 
 one. The methods use techniques\ncoming from Galois representations and mo
 dular forms\; for\nsmall $n$'s one needs Chabauty type methods. Our result
 s\,\nconjectures (and methods) extend those given by Bruin\, Chen\net al. 
 in the case $x^2 + y^{2n} = z^3$. This is a joint work\nwith K. Chałupka 
 and G. Soydan.\n\nMeeting ID: 989 8485 8471\, \nPasscode: 039129\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/6/
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