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 f1, f2, f3 of equal weights k1
... [Show full abstract] = k2 = k3 = k, we study the critical values of Garrett's triple product L(f1 ⊗ f2 ⊗ f3, s, χ) twisted with Dirichlet characters χ. The result is stated in framework of a general program by John Coates, see (Co), (Co-PeRi).