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arXiv · 1505.02711

Singular moduli of higher level and special cycles

Stephan Ehlen
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Abstract

We describe the complex multiplication (CM) values of modular functions for $\Gamma_0(N)$ 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 $\Gamma_0(N)$. By working out explicit formulas for the special cycles, we obtain the prime ideal factorizations of such CM values.

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Stephan Ehlen. 2015-05-11. Singular moduli of higher level and special cycles. https://arxiv.org/abs/1505.02711

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