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Zbl 0808.11035
Dabrowski, Andrzej
$p$-adic $L$-functions of Hilbert modular forms. (English)
[J] Ann. Inst. Fourier 44, No.4, 1025-1041 (1994). ISSN 0373-0956; ISSN 1777-5310/e

Summary: 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 an explicit form of Fourier coefficients of Eisenstein series.

MSC 2000:: *11F67 Special values of automorphic L-series, etc
11F85 p-adic theory, local fields
11S80 Other analytic theory of local fields

Keywords: $p$-adic $L$-function; Hilbert cusp form; complex-valued distribution; growth distribution; growth condition; non-archimedean Mellin transform

Cited in: Zbl 1219.11135

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