Abc conjecture (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Abc conjecture" in English language version.

refsWebsite

Global rank English rank

12doi.org

2^nd place

5semanticscholar.org

11^th place

8^th place

5kyoto-u.ac.jp

2,913^th place

5,132^nd place

4zbmath.org

1,923^rd place

1,068^th place

4web.archive.org

1^st place

3harvard.edu

18^th place

17^th place

3ams.org

451^st place

277^th place

2worldcat.org

5^th place

2nih.gov

4^th place

2columbia.edu

488^th place

374^th place

2umontreal.ca

6,223^rd place

6,135^th place

1numdam.org

8,650^th place

7,668^th place

1jstor.org

26^th place

20^th place

1nature.com

234^th place

397^th place

1imj-prg.fr

low place

1uu.nl

2,467^th place

2,049^th place

1ucalgary.ca

3,395^th place

2,576^th place

1archive.org

6^th place

1unipr.it

low place

1arxiv.org

69^th place

59^th place

1rekenmeemetabc.nl

low place

1abcathome.com

low place

1leidenuniv.nl

4,798^th place

4,535^th place

1galoisrepresentations.wordpress.com

low place

1newscientist.com

774^th place

716^th place

1inference-review.com

low place

1mathbabe.org

low place

1quantamagazine.org

6,413^th place

4,268^th place

1ems-ph.org

low place

abcathome.com (Global: low place; English: low place)

"Data collected sofar", ABC@Home, archived from the original on May 15, 2014, retrieved April 30, 2014

ams.org (Global: 451^st place; English: 277^th place)

mathscinet.ams.org

Oesterlé 1988. Oesterlé, Joseph (1988), "Nouvelles approches du "théorème" de Fermat", Astérisque, Séminaire Bourbaki exp 694 (161): 165–186, ISSN 0303-1179, MR 0992208
Pasten, Hector (2017), "Definability of Frobenius orbits and a result on rational distance sets", Monatshefte für Mathematik, 182 (1): 99–126, doi:10.1007/s00605-016-0973-2, MR 3592123, S2CID 7805117

ams.org

Granville, Andrew; Tucker, Thomas (2002). "It's As Easy As abc" (PDF). Notices of the AMS. 49 (10): 1224–1231.

archive.org (Global: 6^th place; English: 6^th place)

Browkin (2000, p. 10) Browkin, Jerzy (2000). "The abc-conjecture". In Bambah, R. P.; Dumir, V. C.; Hans-Gill, R. J. (eds.). Number Theory. Trends in Mathematics. Basel: Birkhäuser. pp. 75–106. ISBN 3-7643-6259-6.

arxiv.org (Global: 69^th place; English: 59^th place)

Surroca, Andrea (2004). "Siegel's theorem and the abc conjecture" (PDF). Rivista Matematica dell'Universita' di Parma, Atti del Secondo Convegno Italiano di Teoria dei Numeri. 3* (7): 323–332. arXiv:math/0408168.

columbia.edu (Global: 488^th place; English: 374^th place)

math.columbia.edu

Further comment by P. Scholze at Not Even Wrong math.columbia.edu^{[self-published source?]}
"Finiteness Theorems for Dynamical Systems", Lucien Szpiro, talk at Conference on L-functions and Automorphic Forms (on the occasion of Dorian Goldfeld's 60th Birthday), Columbia University, May 2007. See Woit, Peter (May 26, 2007), "Proof of the abc Conjecture?", Not Even Wrong.

doi.org (Global: 2^nd place; English: 2^nd place)

Goldfeld 1996. Goldfeld, Dorian (1996). "Beyond the last theorem". Math Horizons. 4 (September): 26–34. doi:10.1080/10724117.1996.11974985. JSTOR 25678079.
Fesenko, Ivan (September 2015). "Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta-functions, notes on the work of Shinichi Mochizuki". European Journal of Mathematics. 1 (3): 405–440. doi:10.1007/s40879-015-0066-0.
Ball, Peter (10 September 2012). "Proof claimed for deep connection between primes". Nature. doi:10.1038/nature.2012.11378. Retrieved 19 March 2018.
Castelvecchi, Davide (9 April 2020). "Mathematical proof that rocked number theory will be published". Nature. 580 (7802): 177. Bibcode:2020Natur.580..177C. doi:10.1038/d41586-020-00998-2. PMID 32246118. S2CID 214786566.
Waldschmidt 2015. Waldschmidt, Michel (2015). "Lecture on the abc Conjecture and Some of Its Consequences" (PDF). Mathematics in the 21st Century. Springer Proceedings in Mathematics & Statistics. Vol. 98. pp. 211–230. doi:10.1007/978-3-0348-0859-0_13. ISBN 978-3-0348-0858-3.
Elkies (1991). Elkies, N. D. (1991). "ABC implies Mordell". International Mathematics Research Notices. 1991 (7): 99–109. doi:10.1155/S1073792891000144.
Silverman (1988). Silverman, Joseph H. (1988). "Wieferich's criterion and the abc-conjecture". Journal of Number Theory. 30 (2): 226–237. doi:10.1016/0022-314X(88)90019-4. Zbl 0654.10019.
Granville & Stark (2000). Granville, Andrew; Stark, H. (2000). "ABC implies no "Siegel zeros" for L-functions of characters with negative exponent" (PDF). Inventiones Mathematicae. 139 (3): 509–523. Bibcode:2000InMat.139..509G. doi:10.1007/s002229900036. S2CID 6901166.
Granville (1998). Granville, A. (1998). "ABC Allows Us to Count Squarefrees" (PDF). International Mathematics Research Notices. 1998 (19): 991–1009. doi:10.1155/S1073792898000592.
Pasten, Hector (2017), "Definability of Frobenius orbits and a result on rational distance sets", Monatshefte für Mathematik, 182 (1): 99–126, doi:10.1007/s00605-016-0973-2, MR 3592123, S2CID 7805117
Mochizuki, Shinichi (4 March 2021). "Inter-universal Teichmüller Theory IV: Log-Volume Computations and Set-Theoretic Foundations". Publications of the Research Institute for Mathematical Sciences. 57 (1): 627–723. doi:10.4171/PRIMS/57-1-4. S2CID 3135393.
Castelvecchi, Davide (8 October 2015). "The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof". Nature. 526 (7572): 178–181. Bibcode:2015Natur.526..178C. doi:10.1038/526178a. PMID 26450038.

ems-ph.org (Global: low place; English: low place)

Mochizuki, Shinichi. "Mochizuki's proof of ABC conjecture". Retrieved July 13, 2021.

galoisrepresentations.wordpress.com (Global: low place; English: low place)

Calegari, Frank (December 17, 2017). "The ABC conjecture has (still) not been proved". Retrieved March 17, 2018.

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

Castelvecchi, Davide (9 April 2020). "Mathematical proof that rocked number theory will be published". Nature. 580 (7802): 177. Bibcode:2020Natur.580..177C. doi:10.1038/d41586-020-00998-2. PMID 32246118. S2CID 214786566.
Granville & Stark (2000). Granville, Andrew; Stark, H. (2000). "ABC implies no "Siegel zeros" for L-functions of characters with negative exponent" (PDF). Inventiones Mathematicae. 139 (3): 509–523. Bibcode:2000InMat.139..509G. doi:10.1007/s002229900036. S2CID 6901166.
Castelvecchi, Davide (8 October 2015). "The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof". Nature. 526 (7572): 178–181. Bibcode:2015Natur.526..178C. doi:10.1038/526178a. PMID 26450038.

imj-prg.fr (Global: low place; English: low place)

webusers.imj-prg.fr

Waldschmidt 2015. Waldschmidt, Michel (2015). "Lecture on the abc Conjecture and Some of Its Consequences" (PDF). Mathematics in the 21st Century. Springer Proceedings in Mathematics & Statistics. Vol. 98. pp. 211–230. doi:10.1007/978-3-0348-0859-0_13. ISBN 978-3-0348-0858-3.

inference-review.com (Global: low place; English: low place)

Fesenko, Ivan (28 September 2016). "Fukugen". Inference. 2 (3). Retrieved 30 October 2021.

jstor.org (Global: 26^th place; English: 20^th place)

Goldfeld 1996. Goldfeld, Dorian (1996). "Beyond the last theorem". Math Horizons. 4 (September): 26–34. doi:10.1080/10724117.1996.11974985. JSTOR 25678079.

kyoto-u.ac.jp (Global: 2,913^th place; English: 5,132^nd place)

kurims.kyoto-u.ac.jp

Scholze, Peter; Stix, Jakob. "Why abc is still a conjecture" (PDF). Archived from the original (PDF) on February 8, 2020. Retrieved September 23, 2018. (updated version of their May report Archived 2020-02-08 at the Wayback Machine)
"March 2018 Discussions on IUTeich". Retrieved October 2, 2018. Web-page by Mochizuki describing discussions and linking consequent publications and supplementary material
Mochizuki, Shinichi. "Report on Discussions, Held during the Period March 15 – 20, 2018, Concerning Inter-Universal Teichmüller Theory" (PDF). Retrieved February 1, 2019. the ... discussions ... constitute the first detailed, ... substantive discussions concerning negative positions ... IUTch.
Mochizuki, Shinichi (July 2018). "Comments on the manuscript by Scholze-Stix concerning Inter-Universal Teichmüller Theory" (PDF). S2CID 174791744. Retrieved October 2, 2018.
Mochizuki, Shinichi. "Comments on the manuscript (2018-08 version) by Scholze-Stix concerning Inter-Universal Teichmüller Theory" (PDF). Retrieved October 2, 2018.

leidenuniv.nl (Global: 4,798^th place; English: 4,535^th place)

math.leidenuniv.nl

"100 unbeaten triples". Reken mee met ABC. 2010-11-07.

mathbabe.org (Global: low place; English: low place)

Conrad, Brian (December 15, 2015). "Notes on the Oxford IUT workshop by Brian Conrad". Retrieved March 18, 2018.

nature.com (Global: 234^th place; English: 397^th place)

Ball, Peter (10 September 2012). "Proof claimed for deep connection between primes". Nature. doi:10.1038/nature.2012.11378. Retrieved 19 March 2018.

newscientist.com (Global: 774^th place; English: 716^th place)

Revell, Timothy (September 7, 2017). "Baffling ABC maths proof now has impenetrable 300-page 'summary'". New Scientist.

nih.gov (Global: 4^th place; English: 4^th place)

pubmed.ncbi.nlm.nih.gov

Castelvecchi, Davide (9 April 2020). "Mathematical proof that rocked number theory will be published". Nature. 580 (7802): 177. Bibcode:2020Natur.580..177C. doi:10.1038/d41586-020-00998-2. PMID 32246118. S2CID 214786566.
Castelvecchi, Davide (8 October 2015). "The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof". Nature. 526 (7572): 178–181. Bibcode:2015Natur.526..178C. doi:10.1038/526178a. PMID 26450038.

numdam.org (Global: 8,650^th place; English: 7,668^th place)

Oesterlé 1988. Oesterlé, Joseph (1988), "Nouvelles approches du "théorème" de Fermat", Astérisque, Séminaire Bourbaki exp 694 (161): 165–186, ISSN 0303-1179, MR 0992208

quantamagazine.org (Global: 6,413^th place; English: 4,268^th place)

Klarreich, Erica (September 20, 2018). "Titans of Mathematics Clash Over Epic Proof of ABC Conjecture". Quanta Magazine.

rekenmeemetabc.nl (Global: low place; English: low place)

"Synthese resultaten", RekenMeeMetABC.nl (in Dutch), archived from the original on December 22, 2008, retrieved October 3, 2012.

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Castelvecchi, Davide (9 April 2020). "Mathematical proof that rocked number theory will be published". Nature. 580 (7802): 177. Bibcode:2020Natur.580..177C. doi:10.1038/d41586-020-00998-2. PMID 32246118. S2CID 214786566.
Granville & Stark (2000). Granville, Andrew; Stark, H. (2000). "ABC implies no "Siegel zeros" for L-functions of characters with negative exponent" (PDF). Inventiones Mathematicae. 139 (3): 509–523. Bibcode:2000InMat.139..509G. doi:10.1007/s002229900036. S2CID 6901166.
Pasten, Hector (2017), "Definability of Frobenius orbits and a result on rational distance sets", Monatshefte für Mathematik, 182 (1): 99–126, doi:10.1007/s00605-016-0973-2, MR 3592123, S2CID 7805117
Mochizuki, Shinichi (4 March 2021). "Inter-universal Teichmüller Theory IV: Log-Volume Computations and Set-Theoretic Foundations". Publications of the Research Institute for Mathematical Sciences. 57 (1): 627–723. doi:10.4171/PRIMS/57-1-4. S2CID 3135393.
Mochizuki, Shinichi (July 2018). "Comments on the manuscript by Scholze-Stix concerning Inter-Universal Teichmüller Theory" (PDF). S2CID 174791744. Retrieved October 2, 2018.

ucalgary.ca (Global: 3,395^th place; English: 2,576^th place)

people.ucalgary.ca

Mollin (2009); Mollin (2010, p. 297) Mollin, R.A. (2009). "A note on the ABC-conjecture" (PDF). Far East Journal of Mathematical Sciences. 33 (3): 267–275. ISSN 0972-0871. Zbl 1241.11034. Archived from the original (PDF) on 2016-03-04. Retrieved 2013-06-14. Mollin, Richard A. (2010). Advanced number theory with applications. Boca Raton, FL: CRC Press. ISBN 978-1-4200-8328-6. Zbl 1200.11002.

umontreal.ca (Global: 6,223^rd place; English: 6,135^th place)

dms.umontreal.ca

Granville & Stark (2000). Granville, Andrew; Stark, H. (2000). "ABC implies no "Siegel zeros" for L-functions of characters with negative exponent" (PDF). Inventiones Mathematicae. 139 (3): 509–523. Bibcode:2000InMat.139..509G. doi:10.1007/s002229900036. S2CID 6901166.
Granville (1998). Granville, A. (1998). "ABC Allows Us to Count Squarefrees" (PDF). International Mathematics Research Notices. 1998 (19): 991–1009. doi:10.1155/S1073792898000592.

unipr.it (Global: low place; English: low place)

rivmat.unipr.it

Surroca, Andrea (2004). "Siegel's theorem and the abc conjecture" (PDF). Rivista Matematica dell'Universita' di Parma, Atti del Secondo Convegno Italiano di Teoria dei Numeri. 3* (7): 323–332. arXiv:math/0408168.

uu.nl (Global: 2,467^th place; English: 2,049^th place)

math.uu.nl

The ABC-conjecture, Frits Beukers, ABC-DAY, Leiden, Utrecht University, 9 September 2005.

web.archive.org (Global: 1^st place; English: 1^st place)

Mollin (2009); Mollin (2010, p. 297) Mollin, R.A. (2009). "A note on the ABC-conjecture" (PDF). Far East Journal of Mathematical Sciences. 33 (3): 267–275. ISSN 0972-0871. Zbl 1241.11034. Archived from the original (PDF) on 2016-03-04. Retrieved 2013-06-14. Mollin, Richard A. (2010). Advanced number theory with applications. Boca Raton, FL: CRC Press. ISBN 978-1-4200-8328-6. Zbl 1200.11002.
"Synthese resultaten", RekenMeeMetABC.nl (in Dutch), archived from the original on December 22, 2008, retrieved October 3, 2012.
"Data collected sofar", ABC@Home, archived from the original on May 15, 2014, retrieved April 30, 2014
Scholze, Peter; Stix, Jakob. "Why abc is still a conjecture" (PDF). Archived from the original (PDF) on February 8, 2020. Retrieved September 23, 2018. (updated version of their May report Archived 2020-02-08 at the Wayback Machine)

worldcat.org (Global: 5^th place; English: 5^th place)

search.worldcat.org

Oesterlé 1988. Oesterlé, Joseph (1988), "Nouvelles approches du "théorème" de Fermat", Astérisque, Séminaire Bourbaki exp 694 (161): 165–186, ISSN 0303-1179, MR 0992208
Mollin (2009); Mollin (2010, p. 297) Mollin, R.A. (2009). "A note on the ABC-conjecture" (PDF). Far East Journal of Mathematical Sciences. 33 (3): 267–275. ISSN 0972-0871. Zbl 1241.11034. Archived from the original (PDF) on 2016-03-04. Retrieved 2013-06-14. Mollin, Richard A. (2010). Advanced number theory with applications. Boca Raton, FL: CRC Press. ISBN 978-1-4200-8328-6. Zbl 1200.11002.

zbmath.org (Global: 1,923^rd place; English: 1,068^th place)

Scholze, Peter. "Review of inter-universal Teichmüller Theory I". zbmath open. Retrieved 2025-02-25.
Silverman (1988). Silverman, Joseph H. (1988). "Wieferich's criterion and the abc-conjecture". Journal of Number Theory. 30 (2): 226–237. doi:10.1016/0022-314X(88)90019-4. Zbl 0654.10019.
Mollin (2009); Mollin (2010, p. 297) Mollin, R.A. (2009). "A note on the ABC-conjecture" (PDF). Far East Journal of Mathematical Sciences. 33 (3): 267–275. ISSN 0972-0871. Zbl 1241.11034. Archived from the original (PDF) on 2016-03-04. Retrieved 2013-06-14. Mollin, Richard A. (2010). Advanced number theory with applications. Boca Raton, FL: CRC Press. ISBN 978-1-4200-8328-6. Zbl 1200.11002.
Bombieri & Gubler (2006), p. 404. Bombieri, Enrico; Gubler, Walter (2006). Heights in Diophantine Geometry. New Mathematical Monographs. Vol. 4. Cambridge University Press. ISBN 978-0-521-71229-3. Zbl 1130.11034.

Abc conjecture (English Wikipedia)

abcathome.com (Global: low place; English: low place)

ams.org (Global: 451st place; English: 277th place)

mathscinet.ams.org

ams.org

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 69th place; English: 59th place)

columbia.edu (Global: 488th place; English: 374th place)

math.columbia.edu

doi.org (Global: 2nd place; English: 2nd place)

ems-ph.org (Global: low place; English: low place)

galoisrepresentations.wordpress.com (Global: low place; English: low place)

harvard.edu (Global: 18th place; English: 17th place)

ui.adsabs.harvard.edu

imj-prg.fr (Global: low place; English: low place)

webusers.imj-prg.fr

inference-review.com (Global: low place; English: low place)

jstor.org (Global: 26th place; English: 20th place)

kyoto-u.ac.jp (Global: 2,913th place; English: 5,132nd place)

kurims.kyoto-u.ac.jp

leidenuniv.nl (Global: 4,798th place; English: 4,535th place)

math.leidenuniv.nl

mathbabe.org (Global: low place; English: low place)

nature.com (Global: 234th place; English: 397th place)

newscientist.com (Global: 774th place; English: 716th place)

nih.gov (Global: 4th place; English: 4th place)

pubmed.ncbi.nlm.nih.gov

numdam.org (Global: 8,650th place; English: 7,668th place)

quantamagazine.org (Global: 6,413th place; English: 4,268th place)

rekenmeemetabc.nl (Global: low place; English: low place)

semanticscholar.org (Global: 11th place; English: 8th place)

api.semanticscholar.org

ucalgary.ca (Global: 3,395th place; English: 2,576th place)

people.ucalgary.ca

umontreal.ca (Global: 6,223rd place; English: 6,135th place)

dms.umontreal.ca

unipr.it (Global: low place; English: low place)

rivmat.unipr.it

uu.nl (Global: 2,467th place; English: 2,049th place)

math.uu.nl

web.archive.org (Global: 1st place; English: 1st place)

worldcat.org (Global: 5th place; English: 5th place)

search.worldcat.org

zbmath.org (Global: 1,923rd place; English: 1,068th place)

ams.org (Global: 451^st place; English: 277^th place)

archive.org (Global: 6^th place; English: 6^th place)

arxiv.org (Global: 69^th place; English: 59^th place)

columbia.edu (Global: 488^th place; English: 374^th place)

doi.org (Global: 2^nd place; English: 2^nd place)

harvard.edu (Global: 18^th place; English: 17^th place)

jstor.org (Global: 26^th place; English: 20^th place)

kyoto-u.ac.jp (Global: 2,913^th place; English: 5,132^nd place)

leidenuniv.nl (Global: 4,798^th place; English: 4,535^th place)

nature.com (Global: 234^th place; English: 397^th place)

newscientist.com (Global: 774^th place; English: 716^th place)

nih.gov (Global: 4^th place; English: 4^th place)

numdam.org (Global: 8,650^th place; English: 7,668^th place)

quantamagazine.org (Global: 6,413^th place; English: 4,268^th place)

semanticscholar.org (Global: 11^th place; English: 8^th place)

ucalgary.ca (Global: 3,395^th place; English: 2,576^th place)

umontreal.ca (Global: 6,223^rd place; English: 6,135^th place)

uu.nl (Global: 2,467^th place; English: 2,049^th place)

web.archive.org (Global: 1^st place; English: 1^st place)

worldcat.org (Global: 5^th place; English: 5^th place)

zbmath.org (Global: 1,923^rd place; English: 1,068^th place)