In the paper we prove an explicit formula for the central values of certain Rankin L-functions. These L-functions are L-functions of Hilbert newforms over a totally real field F, twisted by unitary Hecke characters of a totally imaginary quadratic extension of F. The formula generalizes our former result on L-functions twisted by finite characters. It also eliminates the restriction on ramifications of Popa's paper.
Non vanishing of Central values of modular L-functions for Hecke eigenforms of level one
Averages and nonvanishing of central values of triple product $L$-functions
Non-vanishing of central values of certain $L$-functions on ${\rm GL}(2)\times {\rm GL}(3)$
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