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Seminar

Empirical Evidence for an Arithmetic Analogue of Nevanlinna's Five Value Theorem March 07, 2011 (02:00 PM PST - 03:00 PM PST)
Parent Program: -- MSRI: Baker Board Room
Speaker(s) James Weigandt
Description
Location:  Baker Boardroom
Speaker: Jamie Weigandt
Title: Empirical Evidence for an Arithmetic Analogue of Nevanlinna's Five Value Theorem

Abstract:
Nevanlinna's five value theorem says that two meromorphic functions which take on
five values at the same places must be identical. We discuss the Erd\H{o}s-Woods
conjecture, an arithmetic analogue of this theorem which arose from questions
about divisibility asked by P. Erd\H{o}s and questions about definability asked
by J. Robinson. We discuss Langevin's proof that this conjecture would follow from
the ABC conjecture and its connections with the arithmetic of elliptic curves.
Using the arithmetic data gathered by the ABC@Home project, we give effective
versions of Langevin's results and extend the related sequence  A087914 on the OEIS.

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