Special values of anticyclotomic L-functions for modular forms

By Masataka Chida, Ming-Lun Hsieh. Journal für die Reine und Angewandte Mathematik, 2012

65 citations recorded by the source corpus.

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 μ-invariant of these p-adic L-functions and the non-vanishing of central L-values with anticyclotomic twists.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/91612d6ed6d45df263f325e757d79105421dff9c