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Special values of anticyclcotomic Rankin-Selberg L-functions · arXivDesk

1112.1580Dec 7, 2011

Special values of anticyclcotomic Rankin-Selberg L-functions

Ming-Lun Hsieh

Abstract

In this article, we prove an explicit Waldspurger formula for the toric Hilbert modular forms. As an application, we construct a class of anticyclotomic p-adic Rankin-Selberg L-functions for Hilbert modular forms, generalizing the construction of Bertolini, Darmon and Prasanna in the elliptic case. Moreover, building on works of Hida, we give a necessary and sufficient condition when the Iwasawa mu-invariant of this p-adic L-function vanishes and prove a result on the non-vanishing modulo $p$ of central Rankin-Selberg L-values with anticyclotomic twists.

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The paper addresses: Special values of anticyclcotomic Rankin-Selberg L-functions.
In this article, we prove an explicit Waldspurger formula for the toric Hilbert modular forms.