Type: Incollection

On special finite fields

Florian Luca; Igor E. Shparlinski;

Book Title: Arithmetic, geometry, cryptography and coding theory

Editor: Gilles Lachaud, Christophe Ritzenthaler, Michael A. Tsfasman

Abstract:

It has been shown by J.-P. Serre that the largest possible number of F(q)-rational points on curves of small genus over the finite field F, of q elements depends on the divisibility property p vertical bar [2q(1/2)], where p is the characteristic of F(q). In this paper, we obtain upper and lower bounds on the number of prime powers q <= Q which satisfy this condition and which are not perfect squares.