Generalization of the Ford-Zaharescu Theorem

2025/08/13 by Iudelevich, Elizaveta D., Iudelevich, Vitalii V.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.18280

Abstract

We derive an asymptotic formula for the sum H = ∑_{0lt;γk\leqslant T, 1\leqslant k\leqslant m}h(a₁γ₁+a₂γ₂+⋯ + a_mγ_m), where a₁, a₂, …, a_m are integers whose sum equals zero, γ₁, …, γ_m independently run through the imaginary parts of the non-trivial zeros of the Riemann zeta function, each zero occuring in the sum the number of times of its multiplicity, and the function h belongs to some special class.

Citations

• Statistics on Riemann zeros

Related

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• Explicit approximation of the sum of the reciprocal of the imaginary parts of the zeta zeros
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• Some sums over the non-trivial zeros of the Riemann zeta function