Singular moduli of higher level and special cycles
© Ehlen. 2015
Received: 15 February 2015
Accepted: 11 May 2015
Published: 17 August 2015
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.