MCM Members Seminar
Speaker: Dr. Peng Yu (MCM)
Title: CM value formula for orthogonal Shimura variety with application to lambda invariant
Time: 10:30-11:30am, Jan 2, 2020
Place: MCM110
 
Abstract: In 1985, Gross and Zagier discovered a beautiful factorization formula for the norm of difference of singular moduli. This has inspired a lot of interesting work, one of which is the study of CM values of automorphic Green functions on orthogonal or unitary Shimura varieties. Now we generalize the definition of CM cycles beyond the ‘small’ and ‘big’ CM cycles and give a uniform formula in general using the idea of regularized theta lifts. Finally, as an application, we are able to give an explicit factorization formula for the norm of λ((d1+\sqrt{d1})/2) - λ((d2+\sqrt{d2})/2) with λ being the modular lambda invariant under the condition (d1, d2) = 1.