Non-vanishing of twists of $\mathrm{GL}(4)$ $L$-functions
Non-vanishing of twists of $\mathrm{GL}(4)$ $L$-functions
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Liyang Yang, Princeton University
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I will discuss recent work with Maksym Radziwill in which we show that for any fixed tempered cuspidal representation $\pi$ of $\mathrm{GL}(4)$ over the rationals, there exist infinitely many primitive characters $\chi$ such that the twisted $L$-function $L(s,\pi\times\chi)$ is non-vanishing at the central point $s=1/2$. I will focus on the proof, which involves a mix of ideas.
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