DOCUMENTA MATHEMATICA, Vol. Extra Volume: John H. Coates' Sixtieth Birthday (2006), 77-132

Siegfried Böcherer, A. A. Panchishkin

Admissible p-adic Measures Attached to Triple Products of Elliptic Cusp Forms

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 $L(f_1øtimes f_2øtimes f_3, s, \chi)$ twisted with Dirichlet characters $\chi$. The result is stated in framework of a general program by John Coates, see \cite{Co}, \cite{Co-PeRi}.

2000 Mathematics Subject Classification: 11F60, 11S80

Keywords and Phrases: Siegel-Eisenstein series, triple products, admissible measures

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