Abstract
Let $L(\mathop {\rm sym}^jf, s)$ be the $j$th symmetric power $L$-function attached to a holomorphic Hecke eigencuspform $f(z)$ for the full modular group $\Gamma =\mathrm {SL}(2,\mathbb {Z})$, and $\lambda _{\mathop {\rm sym}^jf}(n)$ denote its $n$th Dir
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