Diophantine approximation and transcendence / Approximation diophantienne et transcendance

Collection Diophantine approximation and transcendence / Approximation diophantienne et transcendance

Organizer(s) Adamczewski, Boris ; Bugeaud, Yann ; Habegger, Philipp ; Laurent, Michel ; Zannier, Umberto

Date(s) 10/09/2018 - 14/09/2018

linked URL https://conferences.cirm-math.fr/1841.html

00:00:00 / 00:00:00

6 9

Chapters

A refinement of the abc conjecture

By Cameron L. Stewart

We shall discuss joint work with Robert and Tenenbaum on a proposed refinement of the well known abc conjecture.

Information about the video

Date of recording 15/09/2014
Date of publication 23/09/2014
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18573503
Cite this video Stewart, Cameron L. (15/09/2014). A refinement of the abc conjecture. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18573503
URL https://dx.doi.org/10.24350/CIRM.V.18573503

Domain(s)

Number Theory

Bibliography

A. Baker, Logarithmic forms and the abc-conjecture, in: Number Theory (Diophantine, computational and algebraic aspects), Proceedings of the international conference, Eger, Hungary (K. Györy et al., ed.), de Gruyter, Berlin, 1998, 37-44 - http://dx.doi.org/10.1515/9783110809794.37
A. Baker, Experiments on the abc-conjecture, Publ. Math. Debrecen 65 (2004), 253-260 - http://dx.doi.org/10.5486/pmd
E. Bombieri and W. Gubler, Heights in Diophantine geometry, Cambridge University Press, Cambridge, 2007 - https://www.zbmath.org/?q=an:1130.11034
M. van Frankenhuijsen, Hyperbolic spaces and the abc conjecture, thesis, Katholieke Universiteit Nijmegen, 1995
M. van Frankenhuijsen, A lower bound in the abc conjecture, J. of Number Theory 82 (2000), 91-95 - http://dx.doi.org/10.1006/jnth.1999.2484
M. van Frankenhuijsen, About the ABC conjecture and an alternative, Number theory, analysis and geometry, Springer, New York, 2012, 169-180 - https://www.zbmath.org/?q=an:1267.11034
G. Geuze and B. de Smit, Reken mee met ABC, Nieuw Arch. voor Wiskunde 8 (2007), 26-30 - http://www.nieuwarchief.nl/serie5/pdf/naw5-2007-08-1-026.pdf
A. Granville and T.J. Tucker, It's as easy as abc, Notices of the A.M.S. 49 (2002), 1224-1231 - http://www.ams.org/notices/200210/fea-granville.pdf
D.W. Masser, Open problems, Proc. Symp. Analytic Number Theory, (W.W.L. Chen, ed.), Imperial Coll. London, 1985
C. Pomerance, Computational number theory, Princeton Companion to Mathematics, W.T. Gowers, ed., Princeton U. Press, Princeton, New Jersey, 2008, 348-362 - https://www.zbmath.org/?q=an:1242.00016
Reken mee met ABC, 2012 - http://www.rekenmeemetabc.nl/
O. Robert and G. Tenenbaum, Sur la répartition du noyau d'un entier, Indag. Math. 24 (2013), 802-914 - http://dx.doi.org/10.1016/j.indag.2013.07.007
B. de Smit, 2012 - http://pub.math.leidenuniv.nl/~smitbde/abc/
H. Squalli, Sur la r épartition du noyau d'un entier, Thèse de doctorat de troisime cycle, Universit ?e Nancy I, November 18, 1985
C.L. Stewart and R. Tijdeman, On the Oesterlé-Masser conjecture, Monatshefte Math. 102 (1986), 251-257 - http://dx.doi.org/10.1007/bf01294603
C.L. Stewart and K. Yu, On the abc conjecture, II, Duke Math. Journal 108 (2001), 169-181 - http://dx.doi.org/10.1215/s0012-7094-01-10815-6
G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, third ed., coll. Echelles, Belin, 2008 -

MSC codes

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