### 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 language | English |
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Title of host publication | Arithmetic, geometry, cryptography and coding theory |

Editors | G Lachaud, C Ritzenthaler, MA Tsfasman |

Place of Publication | USA |

Publisher | AMER MATHEMATICAL SOC |

Pages | 163-168 |

Number of pages | 6 |

ISBN (Print) | 9780821847169 |

Publication status | Published - 2009 |

Event | 11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory - Marseilles, France Duration: 5 Nov 2007 → 9 Nov 2007 |

### Publication series

Name | Contemporary Mathematics |
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Publisher | AMER MATHEMATICAL SOC |

Volume | 487 |

ISSN (Print) | 0271-4132 |

### Conference

Conference | 11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory |
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Country | France |

City | Marseilles |

Period | 5/11/07 → 9/11/07 |

### 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.