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= The Erdös-Woods Problem= | = The Erdös-Woods Problem= | ||
| − | The Erdös-Woods problem is a surprisingly far reaching question about integers. I has implications for mathematical logic, [[ABC triples]], [[elliptic curves]], and can be generalized to (affine) [[schemes]]. This generalization provides links between number theory and | + | The Erdös-Woods problem is a surprisingly far reaching question about integers. I has implications for mathematical logic, [[ABC triples]], [[elliptic curves]], and can be generalized to (affine) [[schemes]]. This generalization provides links between number theory and Nevanlinna's value distribution theory in complex analysis. Connections between Nevanlinna theory and number theory have already been emphasized by Lang and Vojta in connections with Roth's theorem. |
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| + | This completely independent connection suggests that the ABC conjecture could stated for the ring of entire functions. I seems plausible that it could even be proven by one of our friendly neighborhood Nevanlinna theorists. | ||
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| + | '''UPDATE:''' Apparently ABC conjecture has already been proven for the field of meromorphic functions. This was part of a recent Séminaire Bourbaki, documented [http://arxiv.org/pdf/0811.3153v1 here]. | ||
Revision as of 10:52, 4 August 2010
The Erdös-Woods Problem
The Erdös-Woods problem is a surprisingly far reaching question about integers. I has implications for mathematical logic, ABC triples, elliptic curves, and can be generalized to (affine) schemes. This generalization provides links between number theory and Nevanlinna's value distribution theory in complex analysis. Connections between Nevanlinna theory and number theory have already been emphasized by Lang and Vojta in connections with Roth's theorem.
This completely independent connection suggests that the ABC conjecture could stated for the ring of entire functions. I seems plausible that it could even be proven by one of our friendly neighborhood Nevanlinna theorists.
UPDATE: Apparently ABC conjecture has already been proven for the field of meromorphic functions. This was part of a recent Séminaire Bourbaki, documented here.
