Abstract
Let k = F q (t), with q odd. In this article we introduce “definite” (with respect to the infinite place of k) Shimura curves over k, and establish Hecke module isomorphisms between their Picard groups and the spaces of Drinfeld type “new” forms of corresponding level. An important application is a function field analogue of Gross formula for the central critical values of Rankin type L-series coming from automorphic cusp forms of Drinfeld type. 2010 Mathematics Subject Classification: 11R58 11G18 11F41 11F67.