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Haruzo Hida has constructed a 3-variable Rankin Helberg \(p\)-adic \(L\)-function. Two of its variables are "weight" variables and one of its variables is the "cyclotomic" variable. Samit Dasgupta has factored a certain restriction of this 3-variable \(p\)-adic \(L\)-function (when the two weight variables are set equal to each other) into a product of a 2-variable \(p\)-adic \(L\)-function (related to the adjoint representation of a Hida family) and the Kubota-Leopoldt \(p\)-adic \(L\)-function. We prove the corresponding result involving Selmer groups that is predicted by the main conjectures. A key technical input is studying the (height one) specialization of Selmer groups.