no. 4
p-adic L-functions of Hilbert modular forms
Annales de l'Institut Fourier, Tome 44 (1994) no. 4, pp. 1025-1041.

On construit des L-fonctions p-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.

We construct p-adic L-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.

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     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},
     mrnumber = {96b:11065},
     zbl = {0808.11035},
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     url = {http://www.numdam.org/articles/10.5802/aif.1425/}
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Dabrowski, Andrzej. $p$-adic $L$-functions of Hilbert modular forms. Annales de l'Institut Fourier, Tome 44 (1994) no. 4, pp. 1025-1041. doi : 10.5802/aif.1425. http://www.numdam.org/articles/10.5802/aif.1425/

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