We construct -adic -functions (in general case unbounded) attached to “motivic" primitive Hilbert cusp forms as a non-archimedean Mellin transform of the corresponding admissible measure. In order to prove the growth conditions of the appropriate complex-valued distributions we represent them as Rankin type representation and use Atkin–Lehner theory and explicit form of Fourier coefficients of Eisenstein series.
On construit des -fonctions -adiques (en général non bornées) associées aux formes paraboliques et primitives de Hilbert. Nous écrivons les distributions appropriées aux valeurs complexes comme des représentations intégrales de Rankin et, pour démontrer les conditions de croissance, nous utilisons la théorie d’Aktin–Lehner et la forme explicite des coefficients de Fourier des séries d’Eisenstein.
@article{AIF_1994__44_4_1025_0, author = {Dabrowski, Andrzej}, title = {$p$-adic $L$-functions of {Hilbert} modular forms}, journal = {Annales de l'Institut Fourier}, pages = {1025--1041}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {44}, number = {4}, year = {1994}, doi = {10.5802/aif.1425}, zbl = {0808.11035}, mrnumber = {96b:11065}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1425/} }
TY - JOUR AU - Dabrowski, Andrzej TI - $p$-adic $L$-functions of Hilbert modular forms JO - Annales de l'Institut Fourier PY - 1994 SP - 1025 EP - 1041 VL - 44 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1425/ DO - 10.5802/aif.1425 LA - en ID - AIF_1994__44_4_1025_0 ER -
%0 Journal Article %A Dabrowski, Andrzej %T $p$-adic $L$-functions of Hilbert modular forms %J Annales de l'Institut Fourier %D 1994 %P 1025-1041 %V 44 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1425/ %R 10.5802/aif.1425 %G en %F AIF_1994__44_4_1025_0
Dabrowski, Andrzej. $p$-adic $L$-functions of Hilbert modular forms. Annales de l'Institut Fourier, Volume 44 (1994) no. 4, pp. 1025-1041. doi : 10.5802/aif.1425. https://aif.centre-mersenne.org/articles/10.5802/aif.1425/
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