Local Heuristics and an Exact Formula for Abelian Surfaces Over Finite Fields
Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 673-691
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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 $f$ .
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
@article{10_4153_CMB_2015_050_8,
author = {Achter, Jeffrey and Williams, Cassandra},
title = {Local {Heuristics} and an {Exact} {Formula} for {Abelian} {Surfaces} {Over} {Finite} {Fields}},
journal = {Canadian mathematical bulletin},
pages = {673--691},
year = {2015},
volume = {58},
number = {4},
doi = {10.4153/CMB-2015-050-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-050-8/}
}
TY - JOUR AU - Achter, Jeffrey AU - Williams, Cassandra TI - Local Heuristics and an Exact Formula for Abelian Surfaces Over Finite Fields JO - Canadian mathematical bulletin PY - 2015 SP - 673 EP - 691 VL - 58 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-050-8/ DO - 10.4153/CMB-2015-050-8 ID - 10_4153_CMB_2015_050_8 ER -
%0 Journal Article %A Achter, Jeffrey %A Williams, Cassandra %T Local Heuristics and an Exact Formula for Abelian Surfaces Over Finite Fields %J Canadian mathematical bulletin %D 2015 %P 673-691 %V 58 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-050-8/ %R 10.4153/CMB-2015-050-8 %F 10_4153_CMB_2015_050_8
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