Special values of anticyclotomic L-functions for modular forms

Abstract

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.

arXiv commentSeveral typos in section 3 and 4 are fixed

Cited by in corpus (2)

• On the p-adic Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields
• On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights