## A p-adic analogue of Schneider's theorem |

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2h+l)gt absolute value adequate upper bound algebraic integer algebraic number field algebraically dependent alog ANALOGUE OF SCHNEIDER'S basis representation circle of radius coefficients introduced complex numbers complex variable conjugates Consider the functions constant wr-tm contain a given converges CORNELL UNIVERSITY LIBRARIES Corollary defined degree g denote derivatives distinct point extension of Q Graduate height homogeneous equations identically zero infinite sequence infinitely many homogeneous integral basis introduced by differentiating irrational large positive Lemma Let h lim sup linear combination log log max log m+1 m+l)st place Mahler main theorem non-negative number constant number of summands P-ADIC ANALOGUE p-adic normal function polynomial powers Proof rational coefficients rational integer real number satisfying Schneider's theorem sequence of points show later solution suff sufficiently large Suppose thesis Thomas More Harrington transcendental zero of order