Measures in the Composite Case
In Chapter 4 we developed the formalism of associated power series for measures on Z p . It is necessary to develop it in general. We do this in the present chapter, which could (and should) have been done immediately following Chapter 4. In all this work, a prime p is given a special role. Values of functions lie in C p . In dealing with this composite case, it is also useful to follow Katz, and associate to a measure not only a power series, but an analytic function on the “formal multiplicative group.” This is explained in §2. The introduction of additional notation to handle this composite case, however, made it worthwhile to separate the two cases. Measures on Z p itself, without the extra d, occur both in their own right, and as auxiliaries to the composite case, so it is useful to have their properties tabulated separately.
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