Under GRH, four twisted Dirichlet L-functions at 1/2 + it are simultaneously non-zero for a positive proportion of characters χ mod q (q prime, sufficiently large); unconditionally, this holds for infinitely many χ but with proportion tending to zero.
Hough,The angle of large values ofL-functions, arXiv: 1304.1241v3
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Simultaneous non-vanishing of Dirichlet L-functions
Under GRH, four twisted Dirichlet L-functions at 1/2 + it are simultaneously non-zero for a positive proportion of characters χ mod q (q prime, sufficiently large); unconditionally, this holds for infinitely many χ but with proportion tending to zero.