Singular moduli of higher level and special cycles

2015/05/11 by Ehlen, Stephan
#11F11 #11G15 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1505.02711

Abstract

We describe the complex multiplication (CM) values of modular functions for Γ₀(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 Γ₀(N). By working out explicit formulas for the special cycles, we obtain the prime ideal factorizations of such CM values.

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