Singular moduli of higher level and special cycles

We describe the complex multiplication (CM) values of modular functions for Γ 0 ( N ) whose divisor is given by a linear combination of Heegner divisors in terms of special cycles on the stack of CM elliptic curves. In particular, our results apply to Borcherds products of weight 0 for Γ 0 ( N ) . B...

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Bibliographic Details
Published in:Research in the mathematical sciences 2015-12, Vol.2 (1), Article 16
Main Author: Ehlen, Stephan
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
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Summary:We describe the complex multiplication (CM) values of modular functions for Γ 0 ( N ) whose divisor is given by a linear combination of Heegner divisors in terms of special cycles on the stack of CM elliptic curves. In particular, our results apply to Borcherds products of weight 0 for Γ 0 ( N ) . By working out explicit formulas for the special cycles, we obtain the prime ideal factorizations of such CM values.
ISSN:2197-9847
2197-9847
DOI:10.1186/s40687-015-0030-0