The Ramanujan Journal

, Volume 41, Issue 1–3, pp 543–561 | Cite as

Parabolic cohomology and multiple Hecke L-values



We derive various identities among the special values of multiple Hecke L-series. We show that linear combinations of multiple Hecke L-values can be expressed as linear combinations of products of the usual Hecke L-series evaluated at the critical points. The period polynomials introduced here are values of 2-cocycles, whereas the classical period polynomials of elliptic modular forms come from the 1-cocycles. We derive the 2-cycle and the 3-cycle relations among them.


Iterated Integral Eichler Integral Period polynomial Multiple Hecke L-value Parabolic cohomology Critical values 

Mathematics Subject Classification

11F67 11F11 



The author would like to thank to Prof. F. Brown, Prof. R. Bruggeman, Prof. K. Mastumoto, and Prof. Y. Manin for their comments and valuable discussions. The author also thanks to referee for the valuable comments, which made our exposition much clearer.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsPohang University of Science and TechnologyPohangKorea

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