On a class of generalized Fermat equations of signature $(2,2n,3)$

Abstract: We will discuss the generalized Fermat equations $Ax^2 + By^{2n} = 4z^3$, assuming (for simplicity) that the class number of the imaginary quadratic field $\mathbb Q(\sqrt{-AB})$ is one. The methods use techniques coming from Galois representations and modular forms; for small $n$'s one needs Chabauty type methods. Our results, conjectures (and methods) extend those given by Bruin, Chen et al. in the case $x^2 + y^{2n} = z^3$. This is a joint work with K. Chałupka and G. Soydan.

algebraic geometrynumber theory

Audience: researchers in the topic

Comments: Meeting ID: 989 8485 8471, Passcode: 039129

FGC-HRI-IPM Number Theory Webinars

Series comments: password is 848084