### Abstract

We extend to the function field setting the heuristic previously developed, by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments and ratios of L-functions defined over number fields. Specifically, we give a heuristic for the moments and ratios of a family of L-functions associated with hyperelliptic curves of genus g over a fixed finite field Fq in the limit as g→ ∞ Like in the number field case, there is a striking resemblance to the corresponding formulae for the characteristic polynomials of random matrices. As an application, we calculate the one-level density for the zeros of these L-functions.

Original language | English |
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Pages (from-to) | 102-148 |

Number of pages | 47 |

Journal | Journal of Number Theory |

Volume | 142 |

DOIs | |

Publication status | Published - 1 Jan 2014 |

### Keywords

- Finite fields
- Function fields
- Hyperelliptic curves
- Moments of quadratic Dirichlet L-functions
- Primary
- Random matrix theory
- Ratios of L-functions
- Secondary

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## Cite this

Andrade, J. C., & Keating, J. P. (2014). Conjectures for the integral moments and ratios of L-functions over function fields.

*Journal of Number Theory*,*142*, 102-148. https://doi.org/10.1016/j.jnt.2014.02.019