Special values of anticyclotomic Rankin–Selberg -functions
Ming-Lun Hsieh
0617 Taiwan
![Special values of anticyclotomic Rankin–Selberg $L$-functions cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-dm-volume-19.png&w=3840&q=90)
Abstract
In this article, we construct a class of anticyclotomic -adic Rankin–Selberg -functions for Hilbert modular forms, generalizing the construction of Brakočevic, Bertolini, Darmon and Prasanna in the elliptic case. Moreover, building on works of Hida, we give a necessary and sufficient criterion for the vanishing of the Iwasawa -invariant of this -adic -function vanishes and prove a result on the non-vanishing modulo of central Rankin–Selberg -values with anticyclotomic twists. These results have future applications to Iwasawa main conjecture for Rankin–Selberg convolution and Iwasawa theory for Heegner cycles.
Cite this article
Ming-Lun Hsieh, Special values of anticyclotomic Rankin–Selberg -functions. Doc. Math. 19 (2014), pp. 709–767
DOI 10.4171/DM/462