p-Adic liftings of the supersingular j-invariants and j-zeros of certain Eisenstein series

Let p>3 be a prime. We consider j-zeros of Eisenstein series Ek of weights k=p−1+Mpa(p2−1) with M,a⩾0 as elements of . If M=0, the j-zeros of Ep−1 belong to Qp(ζp2−1) by Hensel's lemma. Call these j-zeros p-adic liftings of supersingular j-invariants. We show that for every such lifting u there is a j-zero r of Ek such that ordp(r−u)>a. Applications of this result are considered. The proof is based on the techniques of formal groups.