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
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- Journal:
- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 07 November 2024, pp. 1-13
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- Article
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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 
${\mathbb {Q}}({\zeta _8})(T_1,T_2,\ldots ,T_n)$.
