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).
The eighth moment of the Riemann zeta function.J
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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).