Distributions of traces of Frobenius for smooth plane curves over finite fields
Ritzenthaler, Christophe ; Lercier, Reynald ; Rovetta, Florent ; Sijsling, Jeroen ; Smith, Benjamin
HAL, hal-01217995 / Harvested from HAL
Text on HAL
In a previous article, we obtained data on the distribution of traces of Frobenius of non-hyperelliptic genus 3 curves over small finite fields. In the present one, we give a heuristic explanation of these data, by extrapolating from results on the distribution of traces of Frobenius for plane curves whose degree is small with respect to the cardinality of their finite base field. In particular, our methods shed some new light on the asymmetry of the distribution around its mean value, which is related to the Serre obstruction.
Publié le : 2019-07-04
Classification:  [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] 
@article{hal-01217995,
     author = {Ritzenthaler, Christophe and Lercier, Reynald and Rovetta, Florent and Sijsling, Jeroen and Smith, Benjamin},
     title = {Distributions of traces of Frobenius for smooth plane curves over finite fields},
     journal = {HAL},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01217995}
}

Ritzenthaler, Christophe; Lercier, Reynald; Rovetta, Florent; Sijsling, Jeroen; Smith, Benjamin. Distributions of traces of Frobenius for smooth plane curves over finite fields. HAL, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/hal-01217995/