Cohen-Lenstra heuristics

• Milovic, Djordjo. “On the \(16\)-Rank of Class Groups of \(\mathbb{Q}(\sqrt{-8p})\) for \(p\equiv -1\bmod 4\).” arXiv:1511.07127 [math], November 23, 2015. http://arxiv.org/abs/1511.07127.
• Bartel, Alex, and Hendrik W. Lenstra Jr. “Commensurability of Automorphism Groups.” arXiv:1510.02758 [math], October 9, 2015. http://arxiv.org/abs/1510.02758.
• Wood, Melanie Matchett. ‘Random Integral Matrices and the Cohen Lenstra Heuristics’. arXiv:1504.04391 [math], 16 April 2015. http://arxiv.org/abs/1504.04391.
• Boston, Nigel, Michael R. Bush, and Farshid Hajir. “Heuristics for \(p\)-Class Towers of Imaginary Quadratic Fields, with an Appendix by Jonathan Blackhurst.” arXiv:1111.4679 [math], November 20, 2011. http://arxiv.org/abs/1111.4679.

노트

말뭉치

1. Ideas such as these will help fuel discussion on what assumptions on a set of fields is necessary to expect random distribution of class group behavior as the Cohen-Lenstra conjectures predict!
2. At the meeting, we hope to have presentations on the various aspects of the Cohen-Lenstra conjectures described above, including the recent re-thinking of the conjectures by Lenstra himself.
3. "New Computations Concerning the Cohen-Lenstra Heuristics.
4. In this paper we study the compatibility of Cohen–Lenstra heuristics with Leopoldt's Spiegelungssatz (the reflection theorem).
5. He proved the compatibility of the Cohen–Lenstra conjectures with the Spiegelungssatz in the case p=3.
6. We report on computational results indicating that the well-known Cohen–Lenstra–Martinet heuristic for class groups of number fields may fail in many situations.
7. The Cohen-Lenstra heuristics were initially postulated in the early 1980s for the class groups of number fields.
8. The past ten years have seen an explosion of activity surrounding the Cohen-Lenstra heuristics.
9. Moreover Cohen-Lenstra type phenomena have been observed in such diverse areas of pure mathematics as elliptic curves, hyperbolic 3-manifolds, and the Jacobians of graphs.
10. This article deals with the coherence of the model given by the Cohen–Lenstra heuristic philosophy for class groups and also for their generalizations to Tate–Shafarevich groups.
11. The Cohen-Lenstra Heuristics conjecturally give the distribution of class groups of imaginary quadratic fields.