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| In mathematics, '''Siegel's identity''' refers to one of two formulae that are used in the resolution of [[Diophantine equation]]s.
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| ==Statement==
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| The first formula is
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| :<math> \frac{x_3 - x_1}{x_2 - x_1} + \frac{x_2 - x_3}{x_2 - x_1} = 1 . </math> | |
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| The second is
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| :<math> \frac{x_3 - x_1}{x_2 - x_1} \cdot\frac{t - x_2}{t - x_3} + \frac{x_2 - x_3}{x_2 - x_1} \cdot \frac{t - x_1}{t - x_3} = 1 . </math>
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| ==Application==
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| The identities are used in translating Diophantine problems connected with integral points on [[hyperelliptic curve]]s into [[S-unit equation]]s.
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| ==See also==
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| * [[Siegel formula]]
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| ==References==
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| * {{cite book | first=Alan | last=Baker | authorlink=Alan Baker (mathematician) | title=Transcendental Number Theory | publisher=[[Cambridge University Press]] | year=1975 | isbn=0-521-20461-5 | zbl=0297.10013 | page=40 }}
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| * {{cite book | first1=Alan | last1=Baker | authorlink1=Alan Baker (mathematician)| first2=Gisbert | last2= Wüstholz | authorlink2=Gisbert Wüstholz | title=Logarithmic Forms and Diophantine Geometry | series=New Mathematical Monographs | volume=9 | publisher=[[Cambridge University Press]] | year=2007 | isbn=978-0-521-88268-2 | zbl=1145.11004 | page=53 }}
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| * {{cite book | first1=Daniel S. | last1=Kubert | authorlink1=Daniel Kubert | first2=Serge | last2=Lang | authorlink2=Serge Lang | title=Modular Units | series= Grundlehren der Mathematischen Wissenschaften | volume=244 | year=1981 | isbn=0-387-90517-0 }}
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| * {{cite book | first=Serge | last=Lang | authorlink=Serge Lang | title=Elliptic Curves: Diophantine Analysis | volume=231 | series=Grundlehren der mathematischen Wissenschaften | publisher=[[Springer-Verlag]] | year=1978 | isbn=0-387-08489-4 }}
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| * {{cite book | title=The Algorithmic Resolution of Diophantine Equations | volume=41 | series=London Mathematical Society Student Texts | first=N. P. | last=Smart | authorlink=Nigel Smart (cryptographer) | publisher=[[Cambridge University Press]] | year=1998 | isbn=0-521-64633-2 | pages=36–37 }}
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| [[Category:Mathematical identities]]
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| [[Category:Diophantine equations]]
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| {{algebra-stub}}
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Latest revision as of 12:18, 5 May 2014
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