At least 1/9 of zeros of L(s, Π₀ × χ) lie on the critical line for large Q, with new power-saving mean square asymptotics for PGL(3) twists (unconditional if self-dual) and stronger results for PGL(2).
[CIS11] Brian Conrey, Henryk Iwaniec, and Kannan Soundararajan
2 Pith papers cite this work. Polarity classification is still indexing.
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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.
citing papers explorer
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Critical Zeros and Unconditional Mean Value Theorems for twisted $\hbox{PGL}(2)$ and $\hbox{PGL}(3)$ $\mathrm{L}$-functions
At least 1/9 of zeros of L(s, Π₀ × χ) lie on the critical line for large Q, with new power-saving mean square asymptotics for PGL(3) twists (unconditional if self-dual) and stronger results for PGL(2).
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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.