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In this note, we give a detailed proof of an asymptotic for averages ofcoefficients of a class of degree three $L$-functions which can be factorizedas a product of a degree one and a degree two $L$-functions. We emphasize thatwe can break the $1/2$-barrier in the error term, and we get an explicitexponent.

Averages of coefficients of a class of degree 3 L-functions