Abstract
It is shown that some standard results concerning the p-adic L- functions, Lp(χ), ofQ(p-divisibilities of 1/2Lp(χ, s), and congruences for 1/2Lp(χ, t)−1/2Lp(χ, s), s, t∈ℤp) are direct consequences of a general structural theorem, based only on the functional properties of the p-adic pseudo-measures and distributions attached to these Lp-functions (essentially the “eulerian” ones). The method suggests that all such divisibilities and congruences are obtained systematically by this way, and are the best possible (in a standard point of view). In particular, these results improve significantly all the known ones.
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