### Singular moduli for real quadratic fields

Heilbronn Number Theory Seminar

20th February 2019, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

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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