Abstract
In Part I of this paper, we shall define some invariant, called the N-function, of a tame link of 2 components whose linking number is zero. The N-function is one of the extension of the A-invariant by D. Goldsmith [5], hence should be a smooth concordance invariant. The second author has obtained the formula which relates it with the polynomial of Alexander's type A(ML, i; t) defined by J. Milnor [13]. That is,
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