p-Adic liftings of the supersingular j-invariants and j-zeros of certain Eisenstein series |
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Authors: | P Guerzhoy Z Kent |
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Institution: | Department of Mathematics, University of Hawaii, 2565 McCarthy Mall, Honolulu, HI 96822-2273, United States |
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Abstract: | 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. |
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Keywords: | 11F11 11F33 |
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