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 inJournal of mathematical sciences (New York, N.Y.) Vol. 260; no. 2; pp. 175 - 193
Main Author Zinchenko, N. A.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.01.2022
Springer
Springer Nature B.V
Subjects
Asymptotic methods
Mathematics
Mathematics and Statistics
prime number
11D75
trigonometric sum
semiprime number
short interval
binary additive problem
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-022-05682-6

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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.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05682-6