Special Values of Anticyclotomic L-functions Modulo λ

Abstract

The purpose of this article is to generalize some results of Vatsal on studying the special values of Rankin-Selberg L-functions in an anticyclotomic ${\mathbb{Z}}_p$-extension. Let $g$ be a cuspidal Hilbert modular form of parallel weight (2,...,2) and level $\mathcal{N}$ over a totally real field F, and let K/F be a totally imaginary quadratic extension of relative discriminant $\mathcal{D}$. We study the $l$-adic valuation of the special values $L(g,\chi ,\frac{1}{2})$ as χvaries over the ring class characters of K of $\mathcal{P}$-power conductor, for some fixed prime ideal $\mathcal{P}$. We prove our results under the only assumption that the prime to $\mathcal{P}$ part of $\mathcal{N}$ is relatively prime to $\mathcal{D}$.

24 pages

References in corpus (2)

• On anticyclotomic mu-invariants of modular forms
• Averages of central L-values of Hilbert modular forms with an application to subconvexity

Cited by in corpus (1)

• Test vectors and central L-values for GL(2)