A novel method for computing torus amplitudes for ZN orbifolds without the unfolding technique

A novel method for computing torus amplitudes in orbifold compactifications is suggested. It applies universally for every Abelian N orbifold without requiring the unfolding technique. This method follows from the possibility of obtaining integrals over fundamental domains of every Hecke congruence subgroup Γ 0[N] by computing contour integrals over one-dimensional curves uniformly distributed in these domains.