Schrödinger group: Difference between revisions

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The '''Mason–Stothers theorem''', or simply '''Mason's theorem''', is a mathematical [[theorem]] about [[polynomials]], analogous to the [[abc conjecture]] for integers. It is named after [[W. Wilson Stothers]], who published it in 1981,<ref>{{citation|first=W. W.|last=Stothers|title=Polynomial identities and hauptmoduln|journal=Quarterly J. Math. Oxford|series=2|volume=32|year=1981|pages=349–370}}.</ref> and [[R. C. Mason]], who rediscovered it shortly thereafter.<ref>{{citation|last=Mason|first=R. C.|title=Diophantine Equations over Function Fields|location=Cambridge, England|publisher=Cambridge University Press|year=1984|series=London Mathematical Society Lecture Note Series|volume=96}}.</ref>
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The theorem states:
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:Let {{math|''a''(''t'')}}, {{math|''b''(''t'')}}, and {{math|''c''(''t'')}} be [[relatively prime]] polynomials such that {{math|1=''a'' + ''b'' = ''c''}}, with coefficients that are either [[real number]]s or [[complex number]]s. Then
::<math>\max\{\deg(a),\deg(b),\deg(c)\} \le \deg(\operatorname{rad}(abc))-1,</math>
:where {{math|rad(''f'')}} is the polynomial of minimum degree that has the same [[Root of a function|root]]s as {{math|''f''}}, so {{math|deg(rad(''f''))}} gives the number of distinct roots of {{math|''f''}}.<ref>{{cite book | author = Lang, Serge | authorlink = Serge Lang | title = Algebra| publisher = Springer-Verlag | location =New York, Berlin, Heidelberg | year = 2002 | isbn = 0-387-95385-X|page=194}}</ref>
 
==References==
{{reflist}}
 
==External links==
*{{mathworld|urlname=MasonsTheorem|title=Mason's Theorem}}
*[http://topologicalmusings.wordpress.com/2008/03/03/mason-stothers-theorem-and-the-abc-conjecture/ Mason-Stothers Theorem and the ABC Conjecture], Vishal Lama. A cleaned-up version of the proof from Lang's book.
 
{{DEFAULTSORT:Mason-Stothers theorem}}
[[Category:Theorems in algebra]]
[[Category:Polynomials]]

Latest revision as of 17:49, 9 March 2014

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