On CM masses over global function fields.

The purpose of this paper is to study the masses over CM points on Drinfeld–Stuhler modular curves and definite Shimura curves over global function fields. After connecting the CM masses with the modified Hurwitz class numbers, we show that the generating function of these masses is a particular metaplectic theta series. Applying the Poisson summation formula, we are able to describe explicitly the meromorphic continuation of the Mellin transform of the generating theta series. This enables us to derive not only a Gauss-type mean value formula of the average masses in question, but also provides “new” class number relations in the positive characteristic world. [ABSTRACT FROM AUTHOR]