Abstract
Let p > 3 be a prime. We consider j-zeros of Eisenstein series E k of weights k = p − 1 + M p a ( p 2 − 1 ) with M , a ⩾ 0 as elements of Q ¯ p . If M = 0 , the j-zeros of E p − 1 belong to Q p ( ζ p 2 − 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 E k such that ord p ( r − u ) > a . Applications of this result are considered. The proof is based on the techniques of formal groups.
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