On Drinfeld modular forms of higher rank III: The analogue of the k/12-formula

Continuing the work of [8] and [9], we derive an analogue of the classical “k/12-formula” for Drinfeld modular forms of rank r≥2. Here the vanishing order νω(f) of one modular form at some point ω of the complex upper half-plane is replaced by the intersection multiplicity νω(f1,…,fr−1) of r−1 independent Drinfeld modular forms at some point ω of the Drinfeld symmetric space Ωr. We apply the formula to determine the common zeroes of r−1 consecutive Eisenstein series Eqi−1, where n−r