Geodesic
Theta series and function field analogue of Gross formula
Documenta mathematica, Tome 16 (2011), pp. 723-765.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 11R58, 11G18, 11F41, 11F67
Keywords: function field, quaternion algebra, Shimura curve, automorphic form, Hecke operator, special value of $L$-series 
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     title = {Theta series and function field analogue of {Gross} formula},
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Wei, Fu-Tsun; Yu, Jing. Theta series and function field analogue of Gross formula. Documenta mathematica, Tome 16 (2011), pp. 723-765. http://geodesic.mathdoc.fr/item/DOCMA_2011__16__a8/