| Autor: |
Bucur, Alina, David, Chantal, Feigon, Brooke, Kaplan, Nathan, Lalín, Matilde, Ozman, Ekin, Wood, Melanie Matchett |
| Rok vydání: |
2015 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
We study fluctuations in the number of points of $\ell$-cyclic covers of the projective line over the finite field $\mathbb{F}_q$ when $q \equiv 1 \mod \ell$ is fixed and the genus tends to infinity. The distribution is given as a sum of $q+1$ i.i.d. random variables. This was settled for hyperelliptic curves by Kurlberg and Rudnick, while statistics were obtained for certain components of the moduli space of $\ell$-cyclic covers by Bucur, David, Feigon and Lal\'{i}n. In this paper, we obtain statistics for the distribution of the number of points as the covers vary over the full moduli space of $\ell$-cyclic covers of genus $g$. This is achieved by relating $\ell$-covers to cyclic function field extensions, and counting such extensions with prescribed ramification and splitting conditions at a finite number of primes. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
