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One can use Langlands functoriality to eliminate the so-called Siegel zeros of an automorphic $L$-function. For example, Hoffstein-Ramakrishnan (IMRN 1995) proved that the $L$-function of a $GL(n)$ cusp form for $n>1$ has no Siegel zero if all $GL(m)\times GL(n)$ $L$-functions are $GL(mn)$ $L$-functions. There are several unconditional results along this line, e.g. in the same paper it is shown that the $L$-function of a $GL(2)$ cusp form has no Siegel zero.