Add time:08/23/2019         Source:sciencedirect.com

We generalize the definition of CM cycles beyond the ‘small’ and ‘big’ CM ones studied by various authors, such as in [BY09] and [BKY12] and give a uniform formula for the CM values of Green functions associated to these special cycles in general using the idea of regularized theta lifts. Finally, as an application to Siegel 3-fold X2(2), we can compute special values of theta functions and Rosenhain λ-invariants at a CM cycle, which is useful for genus two curve cryptography as in [CDSLY14].

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