## Abstract

Let

*X*be a projective, irreducible, nonsingular algebraic curve over the finite field**F**_{q}with*q*elements and let |*X*(**F**_{q})| and_{g}(*X*) be its number of rational points and genus respectively. The Ihara constant A(q) has been intensively studied during the last decades, and it is defined as the limit superior of |*X*(**F**_{q})|/_{g}(*X*) as the genus of*X*goes to infinity. In 2012 Homma defined an analogue*D*(*q*) of*A*(*q*), where the nonsingularity of*X*is dropped and*(*_{g}*X*) is replaced with the degree of*X*. We will call D(q) Homma’s constant. In this paper, upper and lower bounds for the value of*D*(_{q}) are found.Original language | English |
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Title of host publication | Arithmetic, Geometry, Cryptography, and Coding Theory 2021 |

Volume | 779 |

Publisher | American Mathematical Society |

Publication date | 2022 |

Pages | 33-40 |

ISBN (Print) | 978-1-4704-6794-4 |

Publication status | Published - 2022 |

Event | 18^{th} International Conference Arithmetic, Geometry, Cryptography and Coding Theory - Centre International de Rencontres Mathematiques, Marseille, FranceDuration: 31 May 2021 → 4 Jun 2021 |

### Conference

Conference | 18^{th} International Conference Arithmetic, Geometry, Cryptography and Coding Theory |
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Location | Centre International de Rencontres Mathematiques |

Country/Territory | France |

City | Marseille |

Period | 31/05/2021 → 04/06/2021 |

## Keywords

- Algebraic curve
- Rational points
- Finite field

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