Geodesic
Admissible $p$-adic measures attached to triple products of elliptic cusp forms
Documenta mathematica, John H. Coates' Sixtieth Birthday (2006), pp. 77-132.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We use the Siegel-Eisenstein distributions of degree three, and their higher twists with Dirichlet characters, in order to construct admissible $p$-adic measures attached to the triple products of elliptic cusp forms. We use an integral representation of Garrett's type for triple products of three cusp eigenforms. For a prime $p$ and for three primitive cusp eigenforms $f_1, f_2, f_3$ of equal weights $k_1= k_2= k_3=k$, we study the critical values of Garrett's triple product $L(f_1\times f_2\times f_3, s, \chi)$ twisted with Dirichlet characters $\chi$. The result is stated in the framework of a general program by John Coates [see Sémin. Bourbaki, Vol. 1988/89, 41e année, Exp. No. 701, Astérisque 177--178, 33--59 (1989; Zbl 0706.11064), Adv. Stud. Pure Math. 17, 23--54 (1989; Zbl 0783.11039)].
Classification : 11F85, 11F60, 11F66, 11S80
Keywords: Siegel-Eisenstein series, triple products, admissible measures 
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     author = {B\"ocherer, Siegfried and Panchishkin, A.A.},
     title = {Admissible $p$-adic measures attached to triple products of elliptic cusp forms},
     journal = {Documenta mathematica},
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     volume = {John H. Coates' Sixtieth Birthday},
     year = {2006},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2006__S5__a21/}
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Böcherer, Siegfried; Panchishkin, A.A. Admissible $p$-adic measures attached to triple products of elliptic cusp forms. Documenta mathematica, John H. Coates' Sixtieth Birthday (2006), pp. 77-132. http://geodesic.mathdoc.fr/item/DOCMA_2006__S5__a21/