Geodesic
Local Heuristics and an Exact Formula for Abelian Surfaces Over Finite Fields
Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 673-691

Voir la notice de l'article provenant de la source Cambridge University Press

Consider a quartic $q$ -Weil polynomial $f$ . Motivated by equidistribution considerations, we define, for each prime $\ell$ , a local factor that measures the relative frequency with which $f$ $ \bmod \,\ell $ occurs as the characteristic polynomial of a symplectic similitude over ${{\mathbb{F}}_{\ell }}$ . For a certain class of polynomials, we show that the resulting infinite product calculates the number of principally polarized abelian surfaces over ${{\mathbb{F}}_{q}}$ with Weil polynomial $f$ .
DOI : 10.4153/CMB-2015-050-8
Mots-clés : 14K02, abelian surfaces, finite fields, random matrices 
Achter, Jeffrey; Williams, Cassandra. Local Heuristics and an Exact Formula for Abelian Surfaces Over Finite Fields. Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 673-691. doi: 10.4153/CMB-2015-050-8
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