This page contains links to files containing data related to numerators of zeta functions of some families of hyperelliptic curves over finite fields. More data is expected to accumulate ; the current data set holds information concerning

• Two families of genus 3, with about 120000 curves, over extensions of degree at most 8 of the field with 5 elements.
• A random sample of 1000 curves of genus 49 over the field with 5 elements.
  

♦ Here is a short text explaining the families and the type of data available, and how to read the tables in Pari/GP or in the statistic package R.

♦ Here is the data for the first family (those are plain text files, compressed using GZip because of their size):

Numerators for gp

Normalized frobenius angles for gp

Normalized frobenius angles for R

♦ Here is the data for the second family:

Numerators for gp

Normalized Frobenius angles for gp

Normalized Frobenius angles for R

♦ Here is the data for the sample of curves of genus 49:

Numerators for gp

Normalized Frobenius angles for gp

Smallest Frobenius angles for R

♦ Here is, as an example, the histograms of the distribution of the smallest normalized Frobenius eigenvalue (i.e., the zero closest to the central critical point) for the first family, and for the random sample.

Distribution of the zero closest to the central point for a family of
hyperelliptic curves of genus 3 over F₃₉₀₆₂₅.


Distribution of the zero closest to the central point for a 1000 random
hyperelliptic curves of genus 49 over F₅.