In their paper Singular moduli for real quadratic fields: a rigid analytic approach, Darmon and Vonk introduced rigid meromorphic cocycles, i.e. elements of H^1(SL_2(Z[1/p]), M^x) where M^x is the multiplicative group of rigid meromorphic functions on the p-adic upper-half plane. Their values at RM points belong to narrow ring class fields of real quadratic fiends and behave analogously to CM values of modular functions on SL_2(Z)\H. In this talk I will present some progress towards developing a Shimura-Shintani correspondence in this setting.

Speaker(s): Isabella Negrini (Mcgill University)