Abstract
In this note, we state some refinements of conjectures of Gan-Gross-Prasad and Kudla concerning the central derivatives of L-series and special cycles on Shimura varieties. The analogues of our formulation for special values of L-series are written in terms of invariant linear forms on autormorphic representations defined by integrations of matrix coefficients.
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The author thanks Wee Teck Gan, Benedict Gross, Jianshu Li, Yifeng Liu, Akshay Venkatesh and Wei Zhang for their help in preparation of this note.
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Dedicated to Professor Lo Yang on the Occasion of His 80th Birthday
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Zhang, S. Linear forms, algebraic cycles, and derivatives of L-series. Sci. China Math. 62, 2401–2408 (2019). https://doi.org/10.1007/s11425-019-1589-7
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DOI: https://doi.org/10.1007/s11425-019-1589-7