http://dspace.bsu.edu.ru/handle/123456789/4310| Title: | On prime numbers of special kind on short intervals |
| Authors: | Motkina, N. N. |
| Keywords: | mathematics theory of numbers sprime number Riemann hypothesis Chebyshev function zeta function Abel integral transformation |
| Issue Date: | 2006 |
| Citation: | Motkina, N.N. On prime numbers of special kind on short intervals / N.N. Motkina ; Belgorod State University // Mathematical notes. - 2006. - Vol.79, N6.-P. 848-853. - doi: 10.1007/s11006-006-0095-6 |
| Abstract: | Suppose that the Riemann hypothesis holds. Suppose that ψ₁(x) = ∑ Λ(n), n≤x {(1/2)n¹/ᶜ}<1/2, where c is a real number, 1 < c ≤ 2 . We prove that, for H >N½⁺¹⁰ᵋ, ε > 0 , the following asymptotic formula is valid: ψ₁(N +H) - ψ₁(N) = H/2(1 + O(1/ Nᵋ) ) |
| URI: | http://dspace.bsu.edu.ru/handle/123456789/4310 |
| Appears in Collections: | Статьи из периодических изданий и сборников (на иностранных языках) = Articles from periodicals and collections (in foreign languages) |
| File | Description | Size | Format | |
|---|---|---|---|---|
| Motkina_On prime numbers.pdf | 93.73 kB | Adobe PDF | View/Open |
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