Theta series and function field analogue of Gross formula
Let , with odd. In this article we introduce «definite» (with respect to the infinite place of ) Shimura curves over , 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 -series coming from automorphic cusp forms of Drinfeld type.
Cite this article
Fu-Tsun Wei, Jing Yu, Theta series and function field analogue of Gross formula. Doc. Math. 16 (2011), pp. 723–765DOI 10.4171/DM/350