Special values of anticyclotomic L-functions for modular forms

Details Special values of anticyclotomic L-functions for modular forms Special values of anticyclotomic L-functions for modular forms

2012-04-11

arxiv.org/abs/1204.2427v1

Mathematics

Number Theory

Scientific paper

In this article, we generalize some works of Bertolini-Darmon and Vatsal on anticyclotomic L-functions attached to modular forms of weight two to higher weight case. We construct a class of anticyclotomic p-adic L-functions for ordinary modular forms and derive the functional equation and the interpolation formula at all critical specializations. Moreover, we prove results on the vanishing of mu-invariant of these p-adic L-functions and the non-vanishing of central L-values with anticyclotomic twists.

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