Special values of certain functions of the type are studied where is a motive over a totally real field with coefficients in another field , and
is an Euler product running through maximal ideals of the maximal order of and
being a polynomial with coefficients in . Using the Newton and the Hodge polygons of one formulate a conjectural criterium for the existence of a -adic analytic continuation of the special values. This conjecture is verified in a number of cases related to Hilbert modular forms.
On étudie des valeurs spéciales des fonctions de type où est un motif sur un corps totalement réel à coefficients dans un corps de nombres , et
est un produit eulérien étendu sur tous les idéaux maximaux de l’ordre maximal de et
est un polynôme à coefficients dans . À l’aide des polygones de Newton et de Hodge de on formule des conditions conjecturales de l’existence d’un prolongement -adique analytique de ces valeurs spéciales. On vérifie cette conjecture dans une série d’exemples liés aux formes modulaires de Hilbert.
@article{AIF_1994__44_4_989_0, author = {Panchishkin, Alexei A.}, title = {Motives over totally real fields and $p$-adic $L$-functions}, journal = {Annales de l'Institut Fourier}, pages = {989--1023}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {44}, number = {4}, year = {1994}, doi = {10.5802/aif.1424}, zbl = {0808.11034}, mrnumber = {96e:11087}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1424/} }
TY - JOUR AU - Panchishkin, Alexei A. TI - Motives over totally real fields and $p$-adic $L$-functions JO - Annales de l'Institut Fourier PY - 1994 SP - 989 EP - 1023 VL - 44 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1424/ DO - 10.5802/aif.1424 LA - en ID - AIF_1994__44_4_989_0 ER -
%0 Journal Article %A Panchishkin, Alexei A. %T Motives over totally real fields and $p$-adic $L$-functions %J Annales de l'Institut Fourier %D 1994 %P 989-1023 %V 44 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1424/ %R 10.5802/aif.1424 %G en %F AIF_1994__44_4_989_0
Panchishkin, Alexei A. Motives over totally real fields and $p$-adic $L$-functions. Annales de l'Institut Fourier, Volume 44 (1994) no. 4, pp. 989-1023. doi : 10.5802/aif.1424. https://aif.centre-mersenne.org/articles/10.5802/aif.1424/
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