Special values of anticyclotomic Rankin–Selberg -functions

  • Ming-Lun Hsieh

    0617 Taiwan
Special values of anticyclotomic Rankin–Selberg $L$-functions cover
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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