"Cohen-Lenstra heuristics"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
(→‎노트: 새 문단)
4번째 줄: 4번째 줄:
 
* Boston, Nigel, Michael R. Bush, and Farshid Hajir. “Heuristics for <math>p</math>-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.
 
* Boston, Nigel, Michael R. Bush, and Farshid Hajir. “Heuristics for <math>p</math>-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.
 
[[분류:migrate]]
 
[[분류:migrate]]
 +
 +
== 노트 ==
 +
 +
===말뭉치===
 +
# 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!<ref name="ref_4f1914f6">[https://aimath.org/pastworkshops/classgroups.html ARCC Workshop: The Cohen-Lenstra heuristics for class groups]</ref>
 +
# 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.<ref name="ref_4f1914f6" />
 +
# "New Computations Concerning the Cohen-Lenstra Heuristics.<ref name="ref_f56787b2">[https://projecteuclid.org/euclid.em/1064858787 New Computations Concerning the Cohen-Lenstra Heuristics]</ref>
 +
# In this paper we study the compatibility of Cohen–Lenstra heuristics with Leopoldt's Spiegelungssatz (the reflection theorem).<ref name="ref_375227e4">[https://www.sciencedirect.com/science/article/pii/S0022314X0192699X Cohen–Lenstra Heuristics and the Spiegelungssatz: Number Fields]</ref>
 +
# He proved the compatibility of the Cohen–Lenstra conjectures with the Spiegelungssatz in the case p=3.<ref name="ref_375227e4" />
 +
# 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.<ref name="ref_c311fb32">[https://www.sciencedirect.com/science/article/pii/S0022314X08000504 Cohen–Lenstra heuristic and roots of unity]</ref>
 +
# The Cohen-Lenstra heuristics were initially postulated in the early 1980s for the class groups of number fields.<ref name="ref_9af57b03">[http://www.maths.gla.ac.uk/~abartel/CL/aims.html Conference on Arithmetic Statistics and the Cohen-Lenstra Heuristics]</ref>
 +
# The past ten years have seen an explosion of activity surrounding the Cohen-Lenstra heuristics.<ref name="ref_9af57b03" />
 +
# 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.<ref name="ref_9af57b03" />
 +
# 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.<ref name="ref_964c4e96">[https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/all/164/3/82084/the-cohen-8211-lenstra-heuristics-moments-and-p-j-ranks-of-some-groups The Cohen&#8211;Lenstra heuristics, moments and $p^j$-ranks of some groupsAll]</ref>
 +
# The Cohen-Lenstra Heuristics conjecturally give the distribution of class groups of imaginary quadratic fields.<ref name="ref_9888119e">[https://www.ias.edu/video/puias/2016/1117-MelanieWood Nonabelian Cohen-Lenstra heuristics and function field theorems]</ref>
 +
===소스===
 +
<references />

2021년 2월 21일 (일) 21:46 판

  • 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![1]
  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.[1]
  3. "New Computations Concerning the Cohen-Lenstra Heuristics.[2]
  4. In this paper we study the compatibility of Cohen–Lenstra heuristics with Leopoldt's Spiegelungssatz (the reflection theorem).[3]
  5. He proved the compatibility of the Cohen–Lenstra conjectures with the Spiegelungssatz in the case p=3.[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.[4]
  7. The Cohen-Lenstra heuristics were initially postulated in the early 1980s for the class groups of number fields.[5]
  8. The past ten years have seen an explosion of activity surrounding the Cohen-Lenstra heuristics.[5]
  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.[5]
  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.[6]
  11. The Cohen-Lenstra Heuristics conjecturally give the distribution of class groups of imaginary quadratic fields.[7]

소스

  1. ↑ 1.0 1.1 ARCC Workshop: The Cohen-Lenstra heuristics for class groups
  2. ↑ New Computations Concerning the Cohen-Lenstra Heuristics
  3. ↑ 3.0 3.1 Cohen–Lenstra Heuristics and the Spiegelungssatz: Number Fields
  4. ↑ Cohen–Lenstra heuristic and roots of unity
  5. ↑ 5.0 5.1 5.2 Conference on Arithmetic Statistics and the Cohen-Lenstra Heuristics
  6. ↑ The Cohen–Lenstra heuristics, moments and $p^j$-ranks of some groupsAll
  7. ↑ Nonabelian Cohen-Lenstra heuristics and function field theorems
원본 주소 "https://wiki.mathnt.net/index.php?title=Cohen-Lenstra_heuristics&oldid=52611"