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.
A note on a conjecture of Ng
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this note we give a lower bound for the second moment of a ratio of zeta functions summed over the non-trivial zeros of the Riemann zeta function that is half the size of the conjectured value. Our result is conditional on the assumption of the Riemann Hypothesis and that all the non-trivial zeros of the zeta function are simple.
fields
math.NT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
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.