Fermat curves over finite fields and cyclic subsets in high-dimensional projective spaces

Authors
Korchmaros, G Szonyi, T
Citation
G. Korchmaros et T. Szonyi, Fermat curves over finite fields and cyclic subsets in high-dimensional projective spaces, FINITE F T, 5(2), 1999, pp. 206-217
Citations number
21
Categorie Soggetti
Mathematics
Journal title
FINITE FIELDS AND THEIR APPLICATIONS
ISSN journal
10715797 → ACNP
Volume
5
Issue
2
Year of publication
1999
Pages
206 - 217
Database
ISI
SICI code
1071-5797(199904)5:2<206:FCOFFA>2.0.ZU;2-D
Abstract
Let GF(q) be the Galois field of order q = p(h), and let m greater than or equal to 3 be an integer. An explicit formula for the number of GF(q(m))-ra tional points of the Fermat curve X-n + Y-n + Z(n) = 0 is given when n divi des (q(m) - 1)/(q - 1) and p is sufficiently large with respect to (q(m) - 1)/(n(q - 1)). (C) 1999 Academic Press.