Geodesic
Theta series and function field analogue of Gross formula
Documenta mathematica, Tome 16 (2011), pp. 723-765
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Let k=Fq​(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.
DOI : 10.4171/dm/350
Classification : 11F41, 11F67, 11G18, 11R58
Mots-clés : quaternion algebra, function field, Shimura curve, automorphic form, Hecke operator, special value of L-series 
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     author = {Fu-Tsun Wei and Jing Yu},
     title = {Theta series and function field analogue of {Gross} formula},
     journal = {Documenta mathematica},
     pages = {723--765},
     year = {2011},
     volume = {16},
     doi = {10.4171/dm/350},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/350/}
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Fu-Tsun Wei; Jing Yu. Theta series and function field analogue of Gross formula. Documenta mathematica, Tome 16 (2011), pp. 723-765. doi: 10.4171/dm/350

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