Editing Abc conjecture (section)

==Sources==
{{refbegin|25em}}
*{{cite book | last=Baker | first=Alan | author-link=Alan Baker (mathematician) | chapter=Logarithmic forms and the ''abc''-conjecture | editor-last=Győry | editor-first=Kálmán | title=Number theory. Diophantine, computational and algebraic aspects. Proceedings of the international conference, Eger, Hungary, July 29-August 2, 1996 | location=Berlin | publisher=de Gruyter | pages=37–44 | year=1998 | isbn=3-11-015364-5 | zbl=0973.11047 }}
*{{cite journal | last=Baker | first=Alan | author-link=Alan Baker (mathematician) | title=Experiments on the ''abc''-conjecture | journal=Publicationes Mathematicae Debrecen | volume=65 |issue=3–4 | pages=253–260 | year=2004  | doi=10.5486/PMD.2004.3348 | s2cid=253834357 |url=https://publi.math.unideb.hu/load_pdf.php?p=972 | doi-access=free }}
*{{cite document | first1=Enrico | last1=Bombieri | title=Roth's theorem and the abc-conjecture |type=Preprint | year=1994 | publisher=ETH Zürich }}{{unreliable source?|still only preprint after all these years?|date=January 2022}}
*{{cite book | first1=Enrico | last1=Bombieri | author-link1=Enrico Bombieri | first2=Walter | last2=Gubler | title=Heights in Diophantine Geometry | series=New Mathematical Monographs | volume=4 | publisher=[[Cambridge University Press]] | year=2006 | isbn=978-0-521-71229-3 | zbl=1130.11034 }}
*{{Cite journal |author-link=Jerzy Browkin |first1=Jerzy |last1=Browkin |first2=Juliusz |last2=Brzeziński | title=Some remarks on the ''abc''-conjecture | journal=Math. Comp. | volume=62 | pages=931–939 | year=1994 | doi=10.2307/2153551 | jstor=2153551 | issue=206 |bibcode=1994MaCom..62..931B }}
* {{cite book |last=Browkin |first=Jerzy |chapter=The ''abc''-conjecture |editor1-last=Bambah |editor1-first=R. P. |editor2-last=Dumir |editor2-first=V. C. |editor3-last=Hans-Gill |editor3-first=R. J. |year=2000 |title=Number Theory |url=https://archive.org/details/numbertheory00bamb_636 |url-access=limited |series=Trends in Mathematics |location=Basel |publisher=Birkhäuser |isbn=3-7643-6259-6 |pages=[https://archive.org/details/numbertheory00bamb_636/page/n83 75]–106 }}
*{{Cite journal |first=Andrzej |last=Dąbrowski |title=On the diophantine equation ''x''! + ''A'' = ''y''<sup>2</sup> | journal=Nieuw Archief voor Wiskunde, IV. |volume=14 |pages=321–324 |year=1996 | zbl=0876.11015 }}
*{{Cite journal |last=Elkies |first=N. D. |author-link=Noam Elkies |title=ABC implies Mordell |journal=  International Mathematics Research Notices|volume=1991 |year=1991 |pages=99–109 |doi=10.1155/S1073792891000144 |issue=7 |doi-access= free}}
* {{cite book |last=Frey |first=Gerhard |author-link=Gerhard Frey |chapter=On Ternary Equations of Fermat Type and Relations with Elliptic Curves |title=Modular Forms and Fermat's Last Theorem |location=New York |publisher=Springer |year=1997 |isbn=0-387-94609-8 |pages=527–548 |chapter-url=https://books.google.com/books?id=Va-quzVwtMsC&pg=PA527 }}
*{{cite journal |last=Goldfeld |first=Dorian | author-link=Dorian M. Goldfeld |year=1996 |title=Beyond the last theorem |journal=[[Math Horizons]] |volume=4 |issue=September |pages=26–34 |jstor= 25678079 |doi=10.1080/10724117.1996.11974985 }}
* {{cite book | zbl=1046.11035 | last=Goldfeld | first=Dorian | author-link=Dorian M. Goldfeld | chapter=Modular forms, elliptic curves and the abc-conjecture | editor-last=Wüstholz | editor-first=Gisbert | editor-link=Gisbert Wüstholz | title=A panorama in number theory or The view from Baker's garden. Based on a conference in honor of Alan Baker's 60th birthday, Zürich, Switzerland, 1999 | location=Cambridge | publisher=[[Cambridge University Press]] | pages=128–147 | year=2002 | isbn=0-521-80799-9 }}
* {{cite book |editor1-last=Gowers |editor1-first=Timothy |editor1-link=Timothy Gowers |editor2-last=Barrow-Green |editor2-first=June |editor3-last=Leader |editor3-first=Imre |title=The Princeton Companion to Mathematics |year=2008 |publisher=Princeton University Press |location=Princeton |isbn=978-0-691-11880-2 |pages=[https://archive.org/details/princetoncompani00gowe_360/page/n672 361]–362, 681 |title-link=The Princeton Companion to Mathematics }}
*{{Cite journal |last=Granville |first=A. |author-link=Andrew Granville |year=1998 |title=ABC Allows Us to Count Squarefrees |url=http://www.dms.umontreal.ca/~andrew/PDF/polysq3.pdf |journal=International Mathematics Research Notices |volume=1998 |issue=19 |pages=991–1009 |doi=10.1155/S1073792898000592 |doi-access=free }}
*{{cite journal |last1=Granville |first1=Andrew | author-link=Andrew Granville |last2=Stark |first2=H. |year=2000 |  title=ABC implies no "Siegel zeros" for L-functions of characters with negative exponent | url= http://www.dms.umontreal.ca/~andrew/PDF/NoSiegelfinal.pdf |journal=[[Inventiones Mathematicae]] |volume= 139 |issue=3 |pages=509–523 |doi=10.1007/s002229900036 |bibcode=2000InMat.139..509G |s2cid=6901166 }}
*{{cite journal |last1=Granville |first1=Andrew | author-link=Andrew Granville |last2=Tucker |first2=Thomas |year=2002 |  title=It's As Easy As abc | url= https://www.ams.org/journals/notices/200210/fea-granville.pdf |journal=[[Notices of the AMS]] |volume= 49 | issue=10 |pages=1224–1231 |citeseerx=10.1.1.146.610 }}
* {{cite book |first=Richard K. |last=Guy |author-link=Richard K. Guy |title=Unsolved Problems in Number Theory |publisher=[[Springer-Verlag]] |location=Berlin |year=2004 |isbn=0-387-20860-7 }}
* {{cite encyclopedia |last1=Lando |first1=Sergei K. |first2=Alexander K. |last2=Zvonkin |title=Graphs on Surfaces and Their Applications |publisher=Springer-Verlag |encyclopedia=Encyclopaedia of Mathematical Sciences: Lower-Dimensional Topology II |volume=141 |year=2004 |isbn=3-540-00203-0 }}
*{{Cite journal |last=Langevin |first=M. |year=1993 |title=Cas d'égalité pour le théorème de Mason et applications de la conjecture ''abc''|language=fr |journal=Comptes rendus de l'Académie des sciences |volume=317 |issue=5 |pages=441–444 }}
*{{Cite book | last=Masser | first=D. W. | author-link=David Masser | editor1-last=Chen | editor1-first=W. W. L. | title=Proceedings of the Symposium on Analytic Number Theory | publisher=Imperial College | location=London | year=1985 | chapter=Open problems}}
*{{cite journal | last=Mollin | first=R.A. | title=A note on the ABC-conjecture | journal=Far East Journal of Mathematical Sciences | volume=33 | number=3 | pages=267–275 | year=2009 | issn=0972-0871 | url=http://people.ucalgary.ca/~ramollin/abcconj.pdf | zbl=1241.11034 | access-date=2013-06-14 | archive-url=https://web.archive.org/web/20160304053930/http://people.ucalgary.ca/~ramollin/abcconj.pdf | archive-date=2016-03-04 | url-status=dead }}
*{{cite book | zbl=1200.11002 | last=Mollin | first=Richard A. | title=Advanced number theory with applications | location=Boca Raton, FL | publisher=CRC Press | year=2010 | isbn=978-1-4200-8328-6 }}
*{{Cite journal |last=Nitaj |first=Abderrahmane |title=La conjecture ''abc''|language=fr |journal=Enseign. Math. |volume=42 |issue=1–2 |pages=3–24 |year=1996 }}
*{{Citation | last1=Oesterlé | first1=Joseph | author-link=Joseph Oesterlé | title=Nouvelles approches du "théorème" de Fermat | url= http://www.numdam.org/item?id=SB_1987-1988__30__165_0 | series=Séminaire Bourbaki exp 694 |mr=992208 | year=1988 | journal=Astérisque | issn=0303-1179 | issue=161 | pages=165–186}}
*{{Cite book |last=Pomerance |first=Carl |author-link=Carl Pomerance |chapter=Computational Number Theory |title=The Princeton Companion to Mathematics |publisher=Princeton University Press |year=2008 |pages=361–362 }}
*{{Cite journal |last=Silverman |first=Joseph H. | author-link=Joseph H. Silverman | year=1988 |title=Wieferich's criterion and the ''abc''-conjecture |journal=[[Journal of Number Theory]] |volume=30 |issue=2 |pages=226–237 |doi=10.1016/0022-314X(88)90019-4 | zbl=0654.10019  |doi-access=free }}
*{{Cite journal |last1=Robert|first1=Olivier |last2 =Stewart|first2=Cameron L.|author2-link=Cameron Leigh Stewart |last3=Tenenbaum|first3=Gérald|author3-link=Gérald Tenenbaum |year=2014 |title=A refinement of the abc conjecture |journal=[[Bulletin of the London Mathematical Society]] |volume=46 |issue=6 |pages=1156–1166 |doi=10.1112/blms/bdu069|s2cid=123460044 |url=https://hal.archives-ouvertes.fr/hal-01281526/file/abc.pdf }}
* {{cite journal |last1=Robert |first1=Olivier |last2=Tenenbaum |first2=Gérald |title=Sur la répartition du noyau d'un entier |trans-title=On the distribution of the kernel of an integer |language=fr |journal=Indagationes Mathematicae |date=November 2013 |volume=24 |issue=4 |pages=802–914 |doi=10.1016/j.indag.2013.07.007 |doi-access=free }}
*{{Cite journal |last1=Stewart |first1=C. L. |author-link=Cameron Leigh Stewart |last2=Tijdeman |first2=R. |author-link2=Robert Tijdeman |year=1986 |title=On the Oesterlé-Masser conjecture |journal=Monatshefte für Mathematik |volume=102 |issue=3 |pages=251–257 |doi=10.1007/BF01294603 |s2cid=123621917 }}
*{{Cite journal |last1=Stewart |first1=C. L. |author-link=Cameron Leigh Stewart|author-link2=Kunrui Yu |first2=Kunrui |last2=Yu |year=1991 |title=On the ''abc'' conjecture |journal=[[Mathematische Annalen]] |volume=291 |issue=1 |pages=225–230 |doi=10.1007/BF01445201 |s2cid=123894587 }}
*{{Cite journal |last1=Stewart |first1=C. L. |author-link=Cameron Leigh Stewart|first2=Kunrui |last2=Yu |author-link2=Kunrui Yu |year=2001 |title=On the ''abc'' conjecture, II |journal=[[Duke Mathematical Journal]] |volume=108 |issue=1 |pages=169–181 |doi=10.1215/S0012-7094-01-10815-6 }}
*{{cite journal | last=van Frankenhuysen | first=Machiel | title=A Lower Bound in the ''abc'' Conjecture | journal=[[J. Number Theory]] | year=2000 | pages=91–95 | volume=82 | issue=1 | mr=1755155 | doi=10.1006/jnth.1999.2484 | doi-access=free }}
*{{cite journal | last=Van Frankenhuijsen | first=Machiel | title=The ABC conjecture implies Vojta's height inequality for curves | journal=[[J. Number Theory]] | year=2002 | pages=289–302 | volume=95 | issue=2 | mr=1924103 | doi=10.1006/jnth.2001.2769 | doi-access=free }}
*{{cite book |doi=10.1007/978-3-0348-0859-0_13|chapter=Lecture on the abc Conjecture and Some of Its Consequences|title=Mathematics in the 21st Century|series=Springer Proceedings in Mathematics & Statistics|year=2015|last1=Waldschmidt|first1=Michel|volume=98|pages=211–230|isbn=978-3-0348-0858-3|chapter-url=https://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/abcLahoreProceedings.pdf}}
{{refend}}