DATE: Tuesday, February 23 (2010), at 12:50pm
PLACE: LIT 305
SPEAKER:
Matthew Boylan (University of South Carolina)
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TITLE:
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The arithmetic-geometric mean and p-adic limits of modular forms
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ABSTRACT:
The arithmetic-geometric mean of Gauss is the coincident limit
of two sequences which arise naturally from systematically taking
arithmetic and geometric means. Gauss proved that these sequences and
their limit, the AGM, are parametrizable by values of modular forms. In
this talk, we will exhibit a sequence of weakly holomorphic modular forms
whose p-adic limit parametrizes values of the AGM. The p-adic limit
arises via the interplay between classical modular forms and harmonic weak
Maass forms. The recent successes connecting harmonic Maass forms to
partitions, Ramanujan's mock theta functions, Lie algebras, probability,
and mathematical physics motivates independent interest in their study.
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