p-adic Mahler measures (with Christopher Deninger, J. Reine Angew. Math. 517 (1999), 19--50)

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We give two p-adic analogues of the classical Mahler measure (for Laurent polynomials in several variables) and study their properties. In the case the polynomial defines an elliptic curve with complex multiplication we are able to relate one of these measures to special values of the associated p-adic L-functions.