A class group heuristic based on the distribution of 1-eigenspaces in matrix groups

JOURNAL OF NUMBER THEORY

卷:149

Article

Adam, Michael¹  Malle, Gunter¹ 

[1] TU Kaiserslautern, FB Math, D-67653 Kaiserslautern, Germany

关键词: Cohen-Lenstra heuristic;    Class groups;    Symplectic groups;    1-Eigenspaces;   

DOI  :  10.1016/j.jnt.2014.10.018

来源: Elsevier

【 摘 要 】

We propose a modification to the Cohen-Lenstraprediction for the distribution of class groups of number fields, which should also apply when the base field contains non-trivial roots of unity. The underlying heuristic derives from the distribution of 1-eigenspaces in certain generalized symplectic groups over finite rings. The motivation for that heuristic comes from the function field case. We also give explicit formulas for the new predictions in several important cases. These are in close accordance with known data. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free