On functional equations of p-adic polylogarithms. Bull. Soc. Math. France , 119 (1991)

Abstract : ABSTRACT . — The n-t h order polylogarithm Ln(z) i s defined by th e series E^Ll zk ''t^ n on tn e Q? 611 un it disc. This functio n has multivalued analytic prolon- gation t o C \ {0,1} . The same series ^^ z k f^ defines an analytic p-adic functio n on th e open uni t disc in Cp (a completion o f an algebraic closure o f Q a t some place above p). The global p-adic analogues o f th e function s L\n(z) are constructed in th e frame o f rigid analysis. These function s are p-adic polylogarithms. In thi s paper we give sufficient and necessary conditions t o have a functiona l equation o f polylogarithms in terms o f maps induced by rational function s on etale fundamenta l groups o f projective lines minus finit e numbers o f points.
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Article dans une revue
Bulletin de de la Société Mathématique de France, 1991, 119 (3)
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https://hal.archives-ouvertes.fr/hal-01293604
Contributeur : Zdzislaw, Jozef Wojtkowiak <>
Soumis le : vendredi 25 mars 2016 - 09:53:05
Dernière modification le : jeudi 31 mars 2016 - 15:30:08

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Zdzislaw, Jozef Wojtkowiak. On functional equations of p-adic polylogarithms. Bull. Soc. Math. France , 119 (1991) . Bulletin de de la Société Mathématique de France, 1991, 119 (3). <hal-01293604>

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