Generalization of the Ford-Zaharescu Theorem

Elizaveta D. Iudelevich; Vitalii V. Iudelevich

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arXiv · 2508.18280

Generalization of the Ford-Zaharescu Theorem

Elizaveta D. Iudelevich·Vitalii V. Iudelevich

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Abstract

We derive an asymptotic formula for the sum $$ H = \sum_{0<\gamma_k\leqslant T,\, 1\leqslant k\leqslant m}h(a_1\gamma_1+a_2\gamma_2+\cdots + a_m\gamma_m), $$ where $a_1, a_2, \ldots, a_m$ are integers whose sum equals zero, $\gamma_1, \ldots, \gamma_m$ 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.

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Elizaveta D. Iudelevich, Vitalii V. Iudelevich. 2025-08-13. Generalization of the Ford-Zaharescu Theorem. https://arxiv.org/abs/2508.18280

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