Generalized heegner cycles and p-adic rankin L-series

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Selmer groups and the indivisibility of Heegner points (2014, methodology): “Skinner then uses a p-adic formula due to Bertolini– Darmon–Prasanna [5] and (one divisibility of) the main conjecture proved by X. Wan [44], while the current paper uses the Gross formula modulo p ([14], an explicit version of Waldspurger formula, cf. §6), the congruence of Bertolini–Darmon [4], an”
Special values of anticyclotomic Rankin-Selberg $L$-functions (2011, methodology): “his is usually referred to as an explicit Waldspurger formula. Such a formula has been exploited widely in the literature based on either explicit theta lifts ([Mur10], [Mur08], [Xue07], [Hid10a] and [BDP]) or the technique of relative trace formula ([MW09]). In this paper we adopt a diﬀerent approa”
A converse to a theorem of Gross, Zagier, and Kolyvagin (2014, background): “Then Lp (f) is the imprimitive variant of the p-adic L-function denoted Lp(f, χ) in [1] (in Case I) and in [6] (in Case II).”