English

On pointless diagonal Fermat curves

Number Theory 2011-05-24 v1

Abstract

We give an improved asymptotic upper bound on the number of diagonal Fermat curves Ax+By=zAx^{\ell}+By^{\ell}=z^{\ell} over Fq\mathbb{F}_{q} with no Fq\mathbb{F}_{q}-rational points, where \ell is a prime number dividing q1q-1.

Keywords

Cite

@article{arxiv.1105.4192,
  title  = {On pointless diagonal Fermat curves},
  author = {Alexander P. McAvoy},
  journal= {arXiv preprint arXiv:1105.4192},
  year   = {2011}
}

Comments

10 pages

R2 v1 2026-06-21T18:10:23.836Z