Linear forms, algebraic cycles, and derivatives of \(L\)-series
In this paper, the author states some refinements of conjectures due to Gan-Gross-Prasad and Kudla, relating central derivatives of automorphic \(L\)-functions to height pairings of special cycles on Shimura varieties. He also considers analogous conjectures for central values where height pairings are replaced by certain invariant linear forms on spaces of automorphic representations. With the inclusion of many references, this short survey article may serve as an overview on recent progress within the very influential circle of ideas relating special values of automorphic \(L\)-functions to the arithmetic geometry of Shimura varieties.
scientific article; zbMATH DE number 7137540
scientific article