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Farid Hosseinijafari : On the Special Values of Certain L-functions: G_2 over a Totally Imaginary Field

In this talk, I will present an overview of the framework originally proposed by Harder and further developed in collaboration with Raghuram to address rationality problems for special values of certain automorphic L-functions. I will then proceed to state my main results on the rationality of the special values of Langlands-Shahidi L-functions appearing in the constant term of the Eisenstein series associated with the exceptional group of type G_2â?? over a totally imaginary number field. This study marks the first instance where rank-one Eisenstein cohomology is employed to investigate the arithmetic of automorphic L-functions in the presence of multiple L-functions.

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