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==관련논문==
 
* Milovic, Djordjo. “On the <math>16</math>-Rank of Class Groups of <math>\mathbb{Q}(\sqrt{-8p})</math> for <math>p\equiv -1\bmod 4</math>.” arXiv:1511.07127 [math], November 23, 2015. http://arxiv.org/abs/1511.07127.
 
* Milovic, Djordjo. “On the <math>16</math>-Rank of Class Groups of <math>\mathbb{Q}(\sqrt{-8p})</math> for <math>p\equiv -1\bmod 4</math>.” 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.
 
* 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.
 
* 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 <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.
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[[분류:migrate]]
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== 노트 ==
 
== 노트 ==
  
 
===말뭉치===
 
===말뭉치===
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# 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>
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# "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>
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# This thesis is devoted to studying this Cohen-Lenstra heuristic.<ref name="ref_e3f6a218">[https://www.math.uni-sb.de/ag/gekeler/PERSONEN/Lengler/Dissertation_Lengler.pdf The cohen-lenstra heuristic]</ref>
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# point out and study a deep connection between the Cohen-Lenstra  probability measure and partitions.<ref name="ref_e3f6a218" />
 +
# show the dierence between the local (i.e., for p-groups) and the global Cohen-Lenstra measure.<ref name="ref_e3f6a218" />
 +
# give applications of the Cohen-Lenstra measure to various elds of mathematics.<ref name="ref_e3f6a218" />
 
# 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>
 
# 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" />
 
# 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" />
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# "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>
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# 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.<ref name="ref_01ef50f4">[https://www.emis.de/journals/EM/expmath/volumes/12/12.1/pp99_113.pdf New computations concerning]</ref>
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# 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>
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# L  L  te Riele and Williams: New Computations Concerning the Cohen-Lenstra Heuristics 103  (2) For i = 1, 2, . . .<ref name="ref_01ef50f4" />
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# He proved the compatibility of the Cohen–Lenstra conjectures with the Spiegelungssatz in the case p=3.<ref name="ref_375227e4" />
 
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# 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 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" />
 
# 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" />
 
# 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" />
 +
# In this note we propose an analog of the well-known Cohen-Lenstra heuristics for modules over the Iwasawa algebra .<ref name="ref_2fd9ca1a">[http://www.math.keio.ac.jp/~kurihara/5.ASPMstyle.pdf Iwasawa-cohen-lenstra heuristics]</ref>
 +
# We call sums of this type Cohen-Lenstra sums, or CL sums for short.<ref name="ref_2fd9ca1a" />
 +
# 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.<ref name="ref_2fd9ca1a" />
 +
# 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.<ref name="ref_722e320c">[https://msp.org/ant/2015/9-1/ant-v9-n1-p05-p.pdf Volume 9]</ref>
 +
# 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".<ref name="ref_78dd2668">[https://www.semanticscholar.org/paper/The-Global-Cohen-Lenstra-Heuristic-Lengler/6e136ff660ee6de0510aee7ab52350240dfa467d [PDF] The Global Cohen-Lenstra Heuristic]</ref>
 +
# 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.<ref name="ref_78dd2668" />
 
# 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>
 
# 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>
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# 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>
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# This paper sketches the Cohen-Lenstra philosophy in both cases of class groups and of Tate-Shafarevich groups.<ref name="ref_a14254d4">[http://delaunay.perso.math.cnrs.fr/heuristics_2.pdf Heuristics on class groups and on]</ref>
 +
# In the second section, we recall the Cohen-Lenstra heuristic for class groups.<ref name="ref_a14254d4" />
 +
# The magic of the Cohen-Lenstra heuristic is that it works!<ref name="ref_a14254d4" />
 +
# Cohen and Lenstra proved (cf.<ref name="ref_a14254d4" />
 
===소스===
 
===소스===
 
  <references />
 
  <references />

2021년 2월 22일 (월) 20:08 기준 최신판

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.[1]
  2. "New Computations Concerning the Cohen-Lenstra Heuristics.[2]
  3. This thesis is devoted to studying this Cohen-Lenstra heuristic.[3]
  4. point out and study a deep connection between the Cohen-Lenstra probability measure and partitions.[3]
  5. show the dierence between the local (i.e., for p-groups) and the global Cohen-Lenstra measure.[3]
  6. give applications of the Cohen-Lenstra measure to various elds of mathematics.[3]
  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![4]
  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.[4]
  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.[5]
  10. L L te Riele and Williams: New Computations Concerning the Cohen-Lenstra Heuristics 103 (2) For i = 1, 2, . . .[5]
  11. The Cohen-Lenstra heuristics were initially postulated in the early 1980s for the class groups of number fields.[6]
  12. The past ten years have seen an explosion of activity surrounding the Cohen-Lenstra heuristics.[6]
  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.[6]
  14. In this note we propose an analog of the well-known Cohen-Lenstra heuristics for modules over the Iwasawa algebra .[7]
  15. We call sums of this type Cohen-Lenstra sums, or CL sums for short.[7]
  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.[7]
  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.[8]
  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".[9]
  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.[9]
  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.[10]
  21. This paper sketches the Cohen-Lenstra philosophy in both cases of class groups and of Tate-Shafarevich groups.[11]
  22. In the second section, we recall the Cohen-Lenstra heuristic for class groups.[11]
  23. The magic of the Cohen-Lenstra heuristic is that it works![11]
  24. Cohen and Lenstra proved (cf.[11]

소스

  1. ↑ Cohen–Lenstra heuristic and roots of unity
  2. ↑ New Computations Concerning the Cohen-Lenstra Heuristics
  3. ↑ 3.0 3.1 3.2 3.3 The cohen-lenstra heuristic
  4. ↑ 4.0 4.1 ARCC Workshop: The Cohen-Lenstra heuristics for class groups
  5. ↑ 5.0 5.1 New computations concerning
  6. ↑ 6.0 6.1 6.2 Conference on Arithmetic Statistics and the Cohen-Lenstra Heuristics
  7. ↑ 7.0 7.1 7.2 Iwasawa-cohen-lenstra heuristics
  8. ↑ Volume 9
  9. ↑ 9.0 9.1 [PDF The Global Cohen-Lenstra Heuristic]
  10. ↑ The Cohen–Lenstra heuristics, moments and $p^j$-ranks of some groupsAll
  11. ↑ 11.0 11.1 11.2 11.3 Heuristics on class groups and on

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