Thursday 28 Mar 2019NT Seminar: Singular moduli for real quadratic fields and p-adic mock modular forms

Dr. Jan Vonk - University of Oxford

H103 14:30-15:30

The theory of complex multiplication describes finite abelian extensions of imaginary quadratic number fields using singular moduli, which are special values of modular functions at CM points. I will describe joint work with Henri Darmon in the setting of real quadratic fields, where we construct p-adic analogues of singular moduli through classes of rigid meromorphic cocycles. I will discuss p-adic counterparts for our proposed RM invariants of classical relations between singular moduli and the theory of weak harmonic Maass forms.

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