Cohen-Lenstra heuristics

관련논문

• 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. 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.
2. "New Computations Concerning the Cohen-Lenstra Heuristics.
3. This thesis is devoted to studying this Cohen-Lenstra heuristic.
4. point out and study a deep connection between the Cohen-Lenstra probability measure and partitions.
5. show the dierence between the local (i.e., for p-groups) and the global Cohen-Lenstra measure.
6. give applications of the Cohen-Lenstra measure to various elds of mathematics.
7. 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!
8. 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.
9. In this paper, we develop some fast techniques for evaluating h(p) where p is not very large and provide some computational results in support of the Cohen-Lenstra heuristics.
10. L L te Riele and Williams: New Computations Concerning the Cohen-Lenstra Heuristics 103 (2) For i = 1, 2, . . .
11. The Cohen-Lenstra heuristics were initially postulated in the early 1980s for the class groups of number fields.
12. The past ten years have seen an explosion of activity surrounding the Cohen-Lenstra heuristics.
13. 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.
14. In this note we propose an analog of the well-known Cohen-Lenstra heuristics for modules over the Iwasawa algebra .
15. We call sums of this type Cohen-Lenstra sums, or CL sums for short.
16. We note that in the classical case the observed scarcity of non-cyclic modules occurring in nature (as class groups) may well have led to the Cohen-Lenstra heuristics in the rst place.
17. Cohen, Lenstra and Martinet predicted that the class numbers of such extensions should be coprime to 3 with probability (cid:89) i=2 (1 3i ) .840.
18. The Cohen-Lenstra heuristic is a universal principle that assigns to each group a probability that tells how often this group should occur "in nature".
19. The most important, but not the only, applications are sequences of class groups, which behave like random sequences of groups with respect to the so-called Cohen-Lenstra probability measure.
20. 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.
21. This paper sketches the Cohen-Lenstra philosophy in both cases of class groups and of Tate-Shafarevich groups.
22. In the second section, we recall the Cohen-Lenstra heuristic for class groups.
23. The magic of the Cohen-Lenstra heuristic is that it works!
24. Cohen and Lenstra proved (cf.

메타데이터

Spacy 패턴 목록

• [{'LOWER': 'cohen'}, {'OP': '*'}, {'LOWER': 'lenstra'}, {'LEMMA': 'heuristic'}]
• [{'LOWER': 'cohen'}, {'OP': '*'}, {'LEMMA': 'Lenstra'}]