Scott.Ahlgren

Affiliation: University of Illinois

Title Of Talk: Modular forms modulo squares of primes

Abstract: Modular forms and their congruences have long played an important role in number theory. The theory of modular forms modulo primes p is well understood. Central to this theory is the theta cycle of a modular form, which is the self-repeating structure arising from repeated differentiation. By contrast until now almost nothing is known about the theta cycle modulo squares of primes. I will describe work with Martin Raum, Olav Richter and Amy Woodall in which we determine (asymptotically) 50% of this theta cycle exactly and provide non-trivial bounds for all of it.

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