2025/04/16 by Francesco Maria Saettone, Saettone, Francesco Maria · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Mathematical Identities
paper · pdf · doi:10.48550/arxiv.2504.12131
We prove an equidistribution statement for the reduction of Galois orbits of CM points on the special fiber of a Shimura curve over a totally real field, considering both the split and the ramified case. The main novelty of the ramified case consists in the use of the moduli interpretation of the Cerednik--Drinfeld uniformisation. Our result is achieved by associating to the reduction of CM points certain Hilbert modular forms of weight 3/2 and by analyzing their Fourier coefficients. Moreover, we also deduce the Shimura curves case of the integral version of the André--Oort conjecture.