Sum of short exponential sums with prime numbers
https://doi.org/10.22405/2226-8383-2025-26-3-235-246
Abstract
For sufficiently large integers 𝐾, 𝑥, 𝑦, 𝑞, subject to 𝐾 ⩽ 𝑦 < 𝑥, 𝑛 — fixed natural number, 𝛼 — real, |𝛼 − 𝑎/𝑞|⩽ 1/𝑞^2 , (𝑎, 𝑞) = 1, 𝑞 ⩾ 1, an estimate of the form
which is a strengthening and generalization of I. M. Vinogradov’s theorem on the distribution of fractional parts of {𝛼𝑝}.
About the Author
Firuz Zarulloevich Rakhmonov
A. Juraev Institute of Mathematics of the National Academy of Sciences of Tajikistan
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
References
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Review
For citations:
Rakhmonov F.Z. Sum of short exponential sums with prime numbers. Chebyshevskii Sbornik. 2025;26(3):235-246. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-3-235-246
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