1 results
POINTS ON
$x^4+y^4=z^4$ OVER QUADRATIC EXTENSIONS OF 
${\mathbb {Q}}(\zeta _8)(T_1,T_2,\ldots ,T_n)$
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 111 / Issue 1 / February 2025
- Published online by Cambridge University Press:
- 07 November 2024, pp. 19-31
- Print publication:
- February 2025
-
- Article
-
- You have access
- HTML
- Export citation
-
Ishitsuka et al. [‘Explicit calculation of the mod 4 Galois representation associated with the Fermat quartic’, Int. J. Number Theory 16(4) (2020), 881–905] found all points on the Fermat quartic
${F_4\colon x^4+y^4=z^4}$ over quadratic extensions of 
${\mathbb {Q}}(\zeta _8)$, where 
$\zeta _8$ is the eighth primitive root of unity 
$e^{i\pi /4}$. Using Mordell’s technique, we give an alternative proof for the result of Ishitsuka et al. and extend it to the rational function field 
${\mathbb {Q}}({\zeta _8})(T_1,T_2,\ldots ,T_n)$.
