Geodesic
Special values of anticyclotomic Rankin-Selberg $L$-functions
Documenta mathematica, Tome 19 (2014), pp. 709-767.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article, we construct a class of anticyclotomic $\padic $Rankin-Selberg $L$-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 $\mu$-invariant of this $\padic L$-function vanishes and prove a result on the non-vanishing modulo $p$ of central Rankin-Selberg $L$-values with anticyclotomic twists. These results have future applications to Iwasawa main conjecture for Rankin-Selberg convolution and Iwasawa theory for Heegner cycles.
Classification : 11F67, 11G15
Keywords: Iwasawa theory, p-adic L-functions, mu-invariant 
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     author = {Hsieh, Ming-Lun},
     title = {Special values of anticyclotomic {Rankin-Selberg} $L$-functions},
     journal = {Documenta mathematica},
     pages = {709--767},
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     volume = {19},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a21/}
}
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Hsieh, Ming-Lun. Special values of anticyclotomic Rankin-Selberg $L$-functions. Documenta mathematica, Tome 19 (2014), pp. 709-767. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a21/