Dedicated to Professor Pit-Mann Wong on the occasion of his sixtieth birthday 1. Introduction. Beginning with the work of Osgood, Vojta, and Lang, it has been observed that many statements in Nevanlinna theory closely resemble statements in Diophantine approximation. Qualitatively, in the simplest case, holomorphic curves in a variety X should correspond to infinite sets of integral points on X. A detailed dictionary between Nevanlinna theory and Diophantine approximation has been developed by Vojta [13]. This correspondence has been influential, inspiring conjectures and results in both subjects. Relatively recently, a p-adic analogue of Nevanlinna theory and value distribution theory has been developed, and many analogous results proven. Similar to the correspondence between classical Nevanlinna theory and Diophantine approximation, we discuss here a correspondence between p-adic Nevanlinna theory and certain Diophantine statements over the integers Z or the rational numbers Q. Roughly speaking, at least for certain classes of varieties, a nonconstant p-adic analytic map into a variety X should correspond to an infinite set of Z-integral points on X. We discuss this in the next section, making some observations towards a precise formulation. While we lack such a precise formulation in general, this correspondence already appears to be useful in suggesting both results and proofs of statements concerning p-adic analytic maps and integral points on varieties. We illustrate this in the last section, giving several examples of parallel p-adic and arithmetic results. Aside from their illustrative purpose, some of these results may be of independent interest.

Abstract. If f is a non-Archimedean analytic curve in a projective variety X embedded in P N and if D 1 , . . . , D q are hypersurfaces of P N in general position with X, then we prove the defect relation:

A polynomial P(X) in [Formula: see text] is called a strong uniqueness polynomial for meromorphic functions if whenever there exist two non-constant meromorphic functions f and g and a complex non-zero constant c such that P(f) = cP(g), then we must have f = g. In this paper, we give a necessary and sufficient condition for a polynomial to be a strong uniqueness polynomial for meromorphic functions under the assumption that P(X) is injective on the roots of P′(X) = 0.

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