Abstract:

Deligne’s conjecture predicted that the period for the critical values of a symmetric even power L-function of an elliptic modular form is equal to a power of the Petersson norm of the associated modular form. In this talk, we present our result on the algebraicity of the symmetric sixth power L-functions of elliptic modular forms. We show that the period in this case is equal to product of Petersson norms of the associated modular form and certain holomorphic Siegel modular form of degree two. Our result is compatible with Deligne’s conjecture.