Singular Moduli for Real Quadratic Fields: a Rigid Analytic Approach

Abstract

A rigid meromorphic cocycle is a class in the first cohomology of the discrete group Γ := SL2(Z[1/p]) with values in the multiplicative group of non-zero rigid meromorphic functions on the p-adic upper half planeHp := P1(Cp)−P1(Qp). Such a class can be evaluated at the real quadratic irrationalities in Hp, which are referred to as “RM points”. The RM values… (More)

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