### Abstract

Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara’s quantity A(ℓ), for ℓ = p

^{n}with p prime and n > 3 odd. We relate the explicit equations to Drinfeld modular varieties.Original language | English |
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Journal | Moscow Mathematical Journal |

Volume | 15 |

Issue number | 1 |

Pages (from-to) | 1-29 |

ISSN | 1609-3321 |

Publication status | Published - 2015 |

### Keywords

- Curves with many points
- Towers of function fields
- Genus
- Rational places
- Ihara’s constant

## Cite this

Bassa, A., Beelen, P., Garcia, A., & Stichtenoth, H. (2015). Towers of Function Fields over Non-prime Finite Fields.

*Moscow Mathematical Journal*,*15*(1), 1-29.