Short cubic exponential sums over primes |
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| Authors: | Z. Kh. Rakhmonov F. Z. Rakhmonov |
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| Affiliation: | 1.A. Juraev Institute of Mathematics,Academy of Sciences of the Republic of Tajikistan,Dushanbe,Tajikistan |
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| Abstract: | For y ≥ x 4/5 L 8B+151 (where L = log(xq) and B is an absolute constant), a nontrivial estimate is obtained for short cubic exponential sums over primes of the form S 3(α; x, y) = ∑ x?y<n≤x Λ(n)e(αn 3), where α = a/q + θ/q 2, (a, q) = 1, L 32(B+20) < q ≤ y 5 x ?2 L ?32(B+20), |θ| ≤ 1, Λ is the von Mangoldt function, and e(t) = e 2πit. |
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