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Science China Mathematics

, Volume 62, Issue 11, pp 2401–2408 | Cite as

Linear forms, algebraic cycles, and derivatives of L-series

  • Shouwu ZhangEmail author
Articles
  • 39 Downloads

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.

Keywords

linear forms algebraic cycles derivatives L-series 

MSC(2010)

11F67 11J20 14C25 

Notes

Acknowledgements

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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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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