Towards a \mathrm{GL}_n variant of the Hoheisel phenomenon.

Let \pi be a unitary cuspidal automorphic representation of \mathrm {GL}_n over a number field, and let \widetilde {\pi } be contragredient to \pi. We prove effective upper and lower bounds of the correct order in the short interval prime number theorem for the Rankin–Selberg L-function L(s,\pi \times \widetilde {\pi }), extending the work of Hoheisel and Linnik. Along the way, we prove for the first time that L(s,\pi \times \widetilde {\pi }) has an unconditional standard zero-free region apart from a possible Landau–Siegel zero. [ABSTRACT FROM AUTHOR]