Assuming GRH and simple zeros, lower bounds are established for ∑ |L'(ρ,χ)|^{-2} and ∑ |L(2ρ,χ²)/L'(ρ,χ)|² that recover half the conjectured asymptotic when q is fixed and degrade to 1/(2+A) when q = T^A.
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2026 2verdicts
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Conditional lower bound (half the conjectured value) for the second moment of a zeta ratio summed over non-trivial zeros, assuming RH and simple zeros.
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Negative discrete second moments of Dirichlet $L$-functions
Assuming GRH and simple zeros, lower bounds are established for ∑ |L'(ρ,χ)|^{-2} and ∑ |L(2ρ,χ²)/L'(ρ,χ)|² that recover half the conjectured asymptotic when q is fixed and degrade to 1/(2+A) when q = T^A.
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A note on a conjecture of Ng
Conditional lower bound (half the conjectured value) for the second moment of a zeta ratio summed over non-trivial zeros, assuming RH and simple zeros.