On Additive Binary Problems with Semiprime Numbers of a Specific Form

The paper is devoted to methods of solution of binary additive problems with semiprime numbers, which form sufficiently “rare” subsequences of the natural series. Additional conditions are imposed on these numbers; the main condition is belonging to so-called Vinogradov intervals. We solve two probl...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022, Vol.260 (2), p.175-193
Main Author: Zinchenko, N. A.
Format: Article
Language:English
Subjects:
Asymptotic methods
Mathematics
Mathematics and Statistics
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Summary:The paper is devoted to methods of solution of binary additive problems with semiprime numbers, which form sufficiently “rare” subsequences of the natural series. Additional conditions are imposed on these numbers; the main condition is belonging to so-called Vinogradov intervals. We solve two problems that are analogs to the Titchmarsh divisor problem; namely, based on the Vinogradov method of trigonometric sums, we obtain asymptotic formulas for the number of solutions to Diophantine equations with semiprime numbers of a specific form.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05682-6