On special finite fields

Florian Luca*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

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

Original languageEnglish
Title of host publicationArithmetic, geometry, cryptography and coding theory
EditorsG Lachaud, C Ritzenthaler, MA Tsfasman
Place of PublicationUSA
PublisherAMER MATHEMATICAL SOC
Pages163-168
Number of pages6
ISBN (Print)9780821847169
Publication statusPublished - 2009
Event11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory - Marseilles, France
Duration: 5 Nov 20079 Nov 2007

Publication series

NameContemporary Mathematics
PublisherAMER MATHEMATICAL SOC
Volume487
ISSN (Print)0271-4132

Conference

Conference11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory
CountryFrance
CityMarseilles
Period5/11/079/11/07

Keywords

  • RATIONAL-POINTS
  • CURVES
  • NUMBER
  • PARTS

Cite this

Luca, F., & Shparlinski, I. E. (2009). On special finite fields. In G. Lachaud, C. Ritzenthaler, & MA. Tsfasman (Eds.), Arithmetic, geometry, cryptography and coding theory (pp. 163-168). (Contemporary Mathematics; Vol. 487). USA: AMER MATHEMATICAL SOC.