考拉兹猜想 (Chinese Wikipedia)

Analysis of information sources in references of the Wikipedia article "考拉兹猜想" in Chinese language version.

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19doi.org

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2quantamagazine.org

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ams.org

Terras, Riho. A stopping time problem on the positive integers (PDF). Acta Arithmetica. 1976, 30 (3): 241–252 [2023-11-12]. MR 0568274. doi:10.4064/aa-30-3-241-252 . （原始内容存档 (PDF)于2023-12-04）.
Krasikov, Ilia; Lagarias, Jeffrey C. Bounds for the 3x + 1 problem using difference inequalities. Acta Arithmetica. 2003, 109 (3): 237–258. Bibcode:2003AcAri.109..237K. MR 1980260. S2CID 18467460. arXiv:math/0205002 . doi:10.4064/aa109-3-4.
Steiner, R. P. A theorem on the syracuse problem. Proceedings of the 7th Manitoba Conference on Numerical Mathematics. 1977: 553–9. MR 0535032.
Simons, John L. On the nonexistence of 2-cycles for the 3x + 1 problem. Math. Comp. 2005, 74: 1565–72. Bibcode:2005MaCom..74.1565S. MR 2137019. doi:10.1090/s0025-5718-04-01728-4 .

archive.org

Lagarias, Jeffrey C. (编). The Ultimate Challenge: The 3x + 1 Problem. American Mathematical Society. 2010. ISBN 978-0-8218-4940-8. Zbl 1253.11003.
Lagarias, Jeffrey C. The 3x + 1 problem and its generalizations. The American Mathematical Monthly. 1985, 92 (1): 3–23. JSTOR 2322189. doi:10.1080/00029890.1985.11971528.
Leavens, Gary T.; Vermeulen, Mike. 3x + 1 search programs. Computers & Mathematics with Applications. December 1992, 24 (11): 79–99. doi:10.1016/0898-1221(92)90034-F .
Bernstein, Daniel J.; Lagarias, Jeffrey C. The 3x + 1 conjugacy map. Canadian Journal of Mathematics. 1996, 48 (6): 1154–1169. ISSN 0008-414X. doi:10.4153/CJM-1996-060-x  （英语）.

arxiv.org

Tao, Terence. Almost all orbits of the Collatz map attain almost bounded values. Forum of Mathematics, Pi. 2022, 10: e12. ISSN 2050-5086. arXiv:1909.03562 . doi:10.1017/fmp.2022.8  （英语）.
Krasikov, Ilia; Lagarias, Jeffrey C. Bounds for the 3x + 1 problem using difference inequalities. Acta Arithmetica. 2003, 109 (3): 237–258. Bibcode:2003AcAri.109..237K. MR 1980260. S2CID 18467460. arXiv:math/0205002 . doi:10.4064/aa109-3-4.
Terence Tao. Almost all orbits of the Collatz map attain almost bounded values. arXiv. 2019-09-13 [2019-12-16]. （原始内容存档于2021-04-17）.

books.google.com

Guy, Richard K. "E16: The 3x+1 problem". Unsolved Problems in Number Theory 3rd. Springer-Verlag. 2004: 330–6 [2023-11-12]. ISBN 0-387-20860-7. Zbl 1058.11001. （原始内容存档于2024-01-21）.
Kurtz, Stuart A.; Simon, Janos. The undecidability of the generalized Collatz problem. Cai, J.-Y.; Cooper, S. B.; Zhu, H. (编). Proceedings of the 4th International Conference on Theory and Applications of Models of Computation, TAMC 2007, held in Shanghai, China in May 2007. 2007: 542–553. ISBN 978-3-540-72503-9. doi:10.1007/978-3-540-72504-6_49. As PDF

cambridge.org

Tao, Terence. Almost all orbits of the Collatz map attain almost bounded values. Forum of Mathematics, Pi. 2022, 10: e12. ISSN 2050-5086. arXiv:1909.03562 . doi:10.1017/fmp.2022.8  （英语）.

doi.org

Lagarias, Jeffrey C. The 3x + 1 problem and its generalizations. The American Mathematical Monthly. 1985, 92 (1): 3–23. JSTOR 2322189. doi:10.1080/00029890.1985.11971528.
Leavens, Gary T.; Vermeulen, Mike. 3x + 1 search programs. Computers & Mathematics with Applications. December 1992, 24 (11): 79–99. doi:10.1016/0898-1221(92)90034-F .
Barina, David. Convergence verification of the Collatz problem. The Journal of Supercomputing. 2020, 77 (3): 2681–2688. S2CID 220294340. doi:10.1007/s11227-020-03368-x.
Garner, Lynn E. On the Collatz 3n + 1 algorithm. Proceedings of the American Mathematical Society. 1981, 82 (1): 19–22. JSTOR 2044308. doi:10.1090/S0002-9939-1981-0603593-2 .
Eliahou, Shalom. The 3x + 1 problem: new lower bounds on nontrivial cycle lengths. Discrete Mathematics. 1993, 118 (1): 45–56. doi:10.1016/0012-365X(93)90052-U .
Simons, J.; de Weger, B. Theoretical and computational bounds for m-cycles of the 3n + 1 problem (PDF). Acta Arithmetica. 2005, 117 (1): 51–70 [2023-11-12]. Bibcode:2005AcAri.117...51S. doi:10.4064/aa117-1-3 . （[35SidW-3n+1-ActaArith[2005].pdf 原始内容] (PDF)存档于2022-03-18）.
Terras, Riho. A stopping time problem on the positive integers (PDF). Acta Arithmetica. 1976, 30 (3): 241–252 [2023-11-12]. MR 0568274. doi:10.4064/aa-30-3-241-252 . （原始内容存档 (PDF)于2023-12-04）.
Tao, Terence. Almost all orbits of the Collatz map attain almost bounded values. Forum of Mathematics, Pi. 2022, 10: e12. ISSN 2050-5086. arXiv:1909.03562 . doi:10.1017/fmp.2022.8  （英语）.
Krasikov, Ilia; Lagarias, Jeffrey C. Bounds for the 3x + 1 problem using difference inequalities. Acta Arithmetica. 2003, 109 (3): 237–258. Bibcode:2003AcAri.109..237K. MR 1980260. S2CID 18467460. arXiv:math/0205002 . doi:10.4064/aa109-3-4.
Simons, John L. On the nonexistence of 2-cycles for the 3x + 1 problem. Math. Comp. 2005, 74: 1565–72. Bibcode:2005MaCom..74.1565S. MR 2137019. doi:10.1090/s0025-5718-04-01728-4 .
Colussi, Livio. The convergence classes of Collatz function. Theoretical Computer Science. 9 September 2011, 412 (39): 5409–5419. doi:10.1016/j.tcs.2011.05.056 .
Hew, Patrick Chisan. Working in binary protects the repetends of 1/3^h: Comment on Colussi's 'The convergence classes of Collatz function'. Theoretical Computer Science. 7 March 2016, 618: 135–141. doi:10.1016/j.tcs.2015.12.033 .
Lagarias, Jeffrey. The set of rational cycles for the 3x+1 problem. Acta Arithmetica. 1990, 56 (1): 33–53 [2023-11-12]. ISSN 0065-1036. doi:10.4064/aa-56-1-33-53 . （原始内容存档于2023-03-27）.
Belaga, Edward G.; Mignotte, Maurice. Embedding the 3x+1 Conjecture in a 3x+d Context. Experimental Mathematics. 1998, 7 (2): 145–151 [2023-11-12]. S2CID 17925995. doi:10.1080/10586458.1998.10504364. （原始内容存档于2023-06-09）.
Bernstein, Daniel J.; Lagarias, Jeffrey C. The 3x + 1 conjugacy map. Canadian Journal of Mathematics. 1996, 48 (6): 1154–1169. ISSN 0008-414X. doi:10.4153/CJM-1996-060-x  （英语）.
Letherman, Simon; Schleicher, Dierk; Wood, Reg. The (3n + 1)-problem and holomorphic dynamics. Experimental Mathematics. 1999, 8 (3): 241–252. doi:10.1080/10586458.1999.10504402.
Garner, Lynn E. On the Collatz 3n + 1 algorithm. Proceedings of the American Mathematical Society. 1981, 82 (1): 19–22. JSTOR 2044308. doi:10.1090/S0002-9939-1981-0603593-2 .
Kurtz, Stuart A.; Simon, Janos. The undecidability of the generalized Collatz problem. Cai, J.-Y.; Cooper, S. B.; Zhu, H. (编). Proceedings of the 4th International Conference on Theory and Applications of Models of Computation, TAMC 2007, held in Shanghai, China in May 2007. 2007: 542–553. ISBN 978-3-540-72503-9. doi:10.1007/978-3-540-72504-6_49. As PDF
Ben-Amram, Amir M. Mortality of iterated piecewise affine functions over the integers: Decidability and complexity. Computability. 2015, 1 (1): 19–56. doi:10.3233/COM-150032.

emis.de

Belaga, Edward G.; Mignotte, Maurice. Embedding the 3x+1 Conjecture in a 3x+d Context. Experimental Mathematics. 1998, 7 (2): 145–151 [2023-11-12]. S2CID 17925995. doi:10.1080/10586458.1998.10504364. （原始内容存档于2023-06-09）.

ericr.nl

Roosendaal, Eric. 3x+1 delay records. [2020-03-14]. （原始内容存档于2023-03-27）. (Note: "Delay records" are total stopping time records.)

eudml.org

Lagarias, Jeffrey. The set of rational cycles for the 3x+1 problem. Acta Arithmetica. 1990, 56 (1): 33–53 [2023-11-12]. ISSN 0065-1036. doi:10.4064/aa-56-1-33-53 . （原始内容存档于2023-03-27）.

harvard.edu

ui.adsabs.harvard.edu

Simons, J.; de Weger, B. Theoretical and computational bounds for m-cycles of the 3n + 1 problem (PDF). Acta Arithmetica. 2005, 117 (1): 51–70 [2023-11-12]. Bibcode:2005AcAri.117...51S. doi:10.4064/aa117-1-3 . （[35SidW-3n+1-ActaArith[2005].pdf 原始内容] (PDF)存档于2022-03-18）.
Krasikov, Ilia; Lagarias, Jeffrey C. Bounds for the 3x + 1 problem using difference inequalities. Acta Arithmetica. 2003, 109 (3): 237–258. Bibcode:2003AcAri.109..237K. MR 1980260. S2CID 18467460. arXiv:math/0205002 . doi:10.4064/aa109-3-4.
Simons, John L. On the nonexistence of 2-cycles for the 3x + 1 problem. Math. Comp. 2005, 74: 1565–72. Bibcode:2005MaCom..74.1565S. MR 2137019. doi:10.1090/s0025-5718-04-01728-4 .

icm.edu.pl

matwbn.icm.edu.pl

Terras, Riho. A stopping time problem on the positive integers (PDF). Acta Arithmetica. 1976, 30 (3): 241–252 [2023-11-12]. MR 0568274. doi:10.4064/aa-30-3-241-252 . （原始内容存档 (PDF)于2023-12-04）.

impan.pl

Krasikov, Ilia; Lagarias, Jeffrey C. Bounds for the 3x + 1 problem using difference inequalities. Acta Arithmetica. 2003, 109 (3): 237–258. Bibcode:2003AcAri.109..237K. MR 1980260. S2CID 18467460. arXiv:math/0205002 . doi:10.4064/aa109-3-4.

jstor.org

Lagarias, Jeffrey C. The 3x + 1 problem and its generalizations. The American Mathematical Monthly. 1985, 92 (1): 3–23. JSTOR 2322189. doi:10.1080/00029890.1985.11971528.
Garner, Lynn E. On the Collatz 3n + 1 algorithm. Proceedings of the American Mathematical Society. 1981, 82 (1): 19–22. JSTOR 2044308. doi:10.1090/S0002-9939-1981-0603593-2 .
Garner, Lynn E. On the Collatz 3n + 1 algorithm. Proceedings of the American Mathematical Society. 1981, 82 (1): 19–22. JSTOR 2044308. doi:10.1090/S0002-9939-1981-0603593-2 .

quantamagazine.org

Hartnett, Kevin. Mathematician Proves Huge Result on ‘Dangerous’ Problem. Quanta Magazine. 2019-12-11 [2023-11-12]. （原始内容存档于2024-01-16）.
Kevin Hartnett. Mathematician Proves Huge Result on ‘Dangerous’ Problem. Quantamagazine. 2019-12-11 [2019-12-16]. （原始内容存档于2020-06-18）.

semanticscholar.org

api.semanticscholar.org

Barina, David. Convergence verification of the Collatz problem. The Journal of Supercomputing. 2020, 77 (3): 2681–2688. S2CID 220294340. doi:10.1007/s11227-020-03368-x.
Krasikov, Ilia; Lagarias, Jeffrey C. Bounds for the 3x + 1 problem using difference inequalities. Acta Arithmetica. 2003, 109 (3): 237–258. Bibcode:2003AcAri.109..237K. MR 1980260. S2CID 18467460. arXiv:math/0205002 . doi:10.4064/aa109-3-4.
Belaga, Edward G.; Mignotte, Maurice. Embedding the 3x+1 Conjecture in a 3x+d Context. Experimental Mathematics. 1998, 7 (2): 145–151 [2023-11-12]. S2CID 17925995. doi:10.1080/10586458.1998.10504364. （原始内容存档于2023-06-09）.

sfu.ca

cecm.sfu.ca

Lagarias (1985) section "A heuristic argument".

uchicago.edu

cs.uchicago.edu

Kurtz, Stuart A.; Simon, Janos. The undecidability of the generalized Collatz problem. Cai, J.-Y.; Cooper, S. B.; Zhu, H. (编). Proceedings of the 4th International Conference on Theory and Applications of Models of Computation, TAMC 2007, held in Shanghai, China in May 2007. 2007: 542–553. ISBN 978-3-540-72503-9. doi:10.1007/978-3-540-72504-6_49. As PDF

unict.it

dmi.unict.it

Scollo, Giuseppe. Looking for class records in the 3x + 1 problem by means of the COMETA grid infrastructure (PDF). Grid Open Days at the University of Palermo. 2007 [2023-11-12]. （原始内容存档 (PDF)于2023-12-09）.

uwaterloo.ca

cs.uwaterloo.ca

Hercher, C. There are no Collatz m-cycles with m <= 91 (PDF). Journal of Integer Sequences. 2023, 26 (3): Article 23.3.5 [2023-11-12]. （原始内容存档 (PDF)于2023-12-08）.

web.archive.org

Guy, Richard K. "E16: The 3x+1 problem". Unsolved Problems in Number Theory 3rd. Springer-Verlag. 2004: 330–6 [2023-11-12]. ISBN 0-387-20860-7. Zbl 1058.11001. （原始内容存档于2024-01-21）.
Roosendaal, Eric. 3x+1 delay records. [2020-03-14]. （原始内容存档于2023-03-27）. (Note: "Delay records" are total stopping time records.)
Simons, J.; de Weger, B. Theoretical and computational bounds for m-cycles of the 3n + 1 problem (PDF). Acta Arithmetica. 2005, 117 (1): 51–70 [2023-11-12]. Bibcode:2005AcAri.117...51S. doi:10.4064/aa117-1-3 . （[35SidW-3n+1-ActaArith[2005].pdf 原始内容] (PDF)存档于2022-03-18）.
Terras, Riho. A stopping time problem on the positive integers (PDF). Acta Arithmetica. 1976, 30 (3): 241–252 [2023-11-12]. MR 0568274. doi:10.4064/aa-30-3-241-252 . （原始内容存档 (PDF)于2023-12-04）.
Hartnett, Kevin. Mathematician Proves Huge Result on ‘Dangerous’ Problem. Quanta Magazine. 2019-12-11 [2023-11-12]. （原始内容存档于2024-01-16）.
Hercher, C. There are no Collatz m-cycles with m <= 91 (PDF). Journal of Integer Sequences. 2023, 26 (3): Article 23.3.5 [2023-11-12]. （原始内容存档 (PDF)于2023-12-08）.
Lagarias, Jeffrey. The set of rational cycles for the 3x+1 problem. Acta Arithmetica. 1990, 56 (1): 33–53 [2023-11-12]. ISSN 0065-1036. doi:10.4064/aa-56-1-33-53 . （原始内容存档于2023-03-27）.
Belaga, Edward G.; Mignotte, Maurice. Embedding the 3x+1 Conjecture in a 3x+d Context. Experimental Mathematics. 1998, 7 (2): 145–151 [2023-11-12]. S2CID 17925995. doi:10.1080/10586458.1998.10504364. （原始内容存档于2023-06-09）.
Scollo, Giuseppe. Looking for class records in the 3x + 1 problem by means of the COMETA grid infrastructure (PDF). Grid Open Days at the University of Palermo. 2007 [2023-11-12]. （原始内容存档 (PDF)于2023-12-09）.
Kevin Hartnett. Mathematician Proves Huge Result on ‘Dangerous’ Problem. Quantamagazine. 2019-12-11 [2019-12-16]. （原始内容存档于2020-06-18）.
Terence Tao. Almost all orbits of the Collatz map attain almost bounded values. arXiv. 2019-09-13 [2019-12-16]. （原始内容存档于2021-04-17）.

worldcat.org

Tao, Terence. Almost all orbits of the Collatz map attain almost bounded values. Forum of Mathematics, Pi. 2022, 10: e12. ISSN 2050-5086. arXiv:1909.03562 . doi:10.1017/fmp.2022.8  （英语）.
Lagarias, Jeffrey. The set of rational cycles for the 3x+1 problem. Acta Arithmetica. 1990, 56 (1): 33–53 [2023-11-12]. ISSN 0065-1036. doi:10.4064/aa-56-1-33-53 . （原始内容存档于2023-03-27）.
Bernstein, Daniel J.; Lagarias, Jeffrey C. The 3x + 1 conjugacy map. Canadian Journal of Mathematics. 1996, 48 (6): 1154–1169. ISSN 0008-414X. doi:10.4153/CJM-1996-060-x  （英语）.

xs4all.nl

deweger.xs4all.nl

Simons, J.; de Weger, B. Theoretical and computational bounds for m-cycles of the 3n + 1 problem (PDF). Acta Arithmetica. 2005, 117 (1): 51–70 [2023-11-12]. Bibcode:2005AcAri.117...51S. doi:10.4064/aa117-1-3 . （[35SidW-3n+1-ActaArith[2005].pdf 原始内容] (PDF)存档于2022-03-18）.

zbmath.org

Guy, Richard K. "E16: The 3x+1 problem". Unsolved Problems in Number Theory 3rd. Springer-Verlag. 2004: 330–6 [2023-11-12]. ISBN 0-387-20860-7. Zbl 1058.11001. （原始内容存档于2024-01-21）.
Lagarias, Jeffrey C. (编). The Ultimate Challenge: The 3x + 1 Problem. American Mathematical Society. 2010. ISBN 978-0-8218-4940-8. Zbl 1253.11003.