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the title is quite explicit: I would like to know the consequences of the degree conjecture for the Selberg class. Thank you in advance.

Let $F$ and $G$ be two primitive functions of the Selberg class, and let $\mathbb{A}$ be the set of values taken by the function which maps a prime number $p$ to $a_{p}(F)\overline{a_{p}(G)}$. $\...