Selberg's normal density theorem for automorphic \(L\)-functions for \(\mathrm{GL}_m\)
Let \(\pi\) be a cuspidal (irreducible, unitary) representation of \(\text{GL}(m,\mathbb A_{\mathbb Q})\), \(m\geq 2\). Let \(L(s,\pi)\) be the \(L\)-function of \(\pi\). Generalizing Selberg's result for the Riemann zeta-function, assuming the Generalized Riemann Hypothesis for \(L(s,\pi)\), the paper estimates the normal density of primes in short intervals for the automorphic \(L\)-function \(L(s,\pi)\), using analytic techniques. see also the author's previous paper [J. Number Theory 122, no. 1, 84--99 (2007; Zbl 1153.11023)]
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