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Pseudo-mesures p- adiques associées aux fonctions L deQ

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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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  1. Faculté des Sciences, Mathématiques, Université de Franche-Comté et C.N.R.S., U.A. C.N.R.S. no 040741, F-25030, Besançon Cedex

    Georges Gras

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  1. Georges Gras
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Gras, G. Pseudo-mesures p- adiques associées aux fonctions L deQ . Manuscripta Math 57, 373–415 (1987). https://doi.org/10.1007/BF01168668

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