Special values of anticyclotomic Rankin-Selberg $L$-functions
By Ming-Lun Hsieh. Documenta Mathematica, 2011
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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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a81fcab71e4c01c8b97fe2561ee6414257dcc025
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Citations in the corpus
- Heegner cycles and p-adic L-functions (2015, background): “er cycles would yield a proof of the implication L′(f,χ,r) 6= 0 = ⇒zf,χ6= 0, which combined with our Theorem B implies conjecture (BK) in the “rank one” case. Appealing to the nonvanishing results of [Hsi14], in Theorem 3.7 we show that the p-adic L-function Lp,ψ(f) ∈Zp[[Γ − K]] is nonzero, and henc”