Geodesic
Special values of anticyclotomic Rankin–Selberg $L$-functions
Documenta mathematica, Tome 19 (2014), pp. 709-767
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In this article, we construct a class of anticyclotomic p-adic 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 μ-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. These results have future applications to Iwasawa main conjecture for Rankin–Selberg convolution and Iwasawa theory for Heegner cycles.
DOI : 10.4171/dm/462
Classification : 11F67, 11G15
Mots-clés : Iwasawa theory, p-adic L-functions, mu-invariant 
@article{10_4171_dm_462,
     author = {Ming-Lun Hsieh},
     title = {Special values of anticyclotomic {Rankin{\textendash}Selberg} $L$-functions},
     journal = {Documenta mathematica},
     pages = {709--767},
     year = {2014},
     volume = {19},
     doi = {10.4171/dm/462},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/462/}
}
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Ming-Lun Hsieh. Special values of anticyclotomic Rankin–Selberg $L$-functions. Documenta mathematica, Tome 19 (2014), pp. 709-767. doi: 10.4171/dm/462

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