Clayton Williams (UIUC): Eisenstein series modulo prime powers

Eisenstein series modulo p are known classically, and recent work of Ahlgren, Hanson, Raum, and Richter determine these series modulo p2. Classical bounds for the weight of a modular form determining an Eisenstein series modulo prime powers pm are roughly pm. I will present joint work with Ahlgren and Castillo showing Eisenstein series are determined modulo pm by a modular form of weight no more than mp, together with an explicit recurrence.

Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).