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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2508.18280 |
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| _version_ | 1866912554422370304 |
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| author | Iudelevich, Elizaveta D. Iudelevich, Vitalii V. |
| author_facet | Iudelevich, Elizaveta D. Iudelevich, Vitalii V. |
| contents | We derive an asymptotic formula for the sum $$ H = \sum_{0<γ_k\leqslant T,\, 1\leqslant k\leqslant m}h(a_1γ_1+a_2γ_2+\cdots + a_mγ_m), $$ where $a_1, a_2, \ldots, a_m$ are integers whose sum equals zero, $γ_1, \ldots, γ_m$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18280 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalization of the Ford-Zaharescu Theorem Iudelevich, Elizaveta D. Iudelevich, Vitalii V. Number Theory We derive an asymptotic formula for the sum $$ H = \sum_{0<γ_k\leqslant T,\, 1\leqslant k\leqslant m}h(a_1γ_1+a_2γ_2+\cdots + a_mγ_m), $$ where $a_1, a_2, \ldots, a_m$ are integers whose sum equals zero, $γ_1, \ldots, γ_m$ 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. |
| title | Generalization of the Ford-Zaharescu Theorem |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.18280 |