On pointless diagonal Fermat curves

Details On pointless diagonal Fermat curves On pointless diagonal Fermat curves

2011-05-20

arxiv.org/abs/1105.4192v1

Mathematics

Number Theory

10 pages

Scientific paper

We give an improved asymptotic upper bound on the number of diagonal Fermat
curves $Ax^{\ell}+By^{\ell}=z^{\ell}$ over $\mathbb{F}_{q}$ with no
$\mathbb{F}_{q}$-rational points, where $\ell$ is a prime number dividing
$q-1$.

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