Some l-adic properties of modular forms with quadratic nebentypus and l-regular partition congruences

Abstract: In this talk, we discuss a framework for studying l-regular partitions by defining a sequence of modular forms of level l and quadratic character which encode the l-adic behavior of the so-called l-regular partitions. We show that this sequence is congruent modulo increasing powers of l to level 1 modular forms of increasing weights. We then prove that certain modules generated by our sequence are isomorphic to certain subspaces of level 1 cusp forms of weight independent of the power of l, leading to a uniform bound on the ranks of those modules and consequently to l-adic relations between l-regular partition values. This generalizes earlier work of Folsom, Kent and Ono on the partition function, where the relevant forms had no nebentypus, and is joint work with Mostafa Ghazy.

algebraic geometrynumber theory

Audience: researchers in the topic

FGC-HRI-IPM Number Theory Webinars

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